{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TP7ReUS8K3iE"
      },
      "source": [
        "# Robust BIM microchip production problem"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "69kabDUFLFPt"
      },
      "outputs": [],
      "source": [
        "# install dependencies and select solver\n",
        "%pip install -q amplpy numpy pandas matplotlib\n",
        "\n",
        "SOLVER_MILP = \"highs\"  # highs, scip, cbc, mosek, gurobi\n",
        "SOLVER_NLO = \"ipopt\"\n",
        "SOLVER_MINLO = \"bonmin\"  # mosek, scip, gurobi, knitro\n",
        "\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"coin\", \"highs\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register notebook magics"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "69kabDUFLFPt"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.patches as patches"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fDTCzz34K3iF"
      },
      "source": [
        "## Original BIM production planning model\n",
        "\n",
        "The full description of the BIM production problem, can be found [here](../02/bim.ipynb). The resulting optimization problem was the following LP:\n",
        "\n",
        "$$\n",
        "\\begin{array}{rrcrcl}\n",
        "\\max    & 12x_1 & + & 9x_2               \\\\\n",
        "\\text{s.t.}    &   x_1 &   &      & \\leq & 1000 \\\\\n",
        "        &       &   &  x_2 & \\leq & 1500 \\\\\n",
        "        &   x_1 & + &  x_2 & \\leq & 1750 \\\\\n",
        "        &  4x_1 & + & 2x_2 & \\leq & 4800 \\\\\n",
        "        &   x_1 & , &  x_2 & \\geq & 0.\n",
        "\\end{array}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "%%ampl_eval\n",
        "\n",
        "set CHIPS;\n",
        "\n",
        "param profits{CHIPS};\n",
        "param copper{CHIPS};\n",
        "\n",
        "var x{CHIPS} >= 0;\n",
        "\n",
        "maximize Profit: sum {c in CHIPS} profits[c] * x[c];\n",
        "\n",
        "s.t. Silicon: x['logic'] <= 1000;\n",
        "s.t. Germanium: x['memory'] <= 1500;\n",
        "s.t. Plastic: sum {c in CHIPS} x[c] <= 1750;\n",
        "s.t. Copper: sum {c in CHIPS} copper[c] * x[c] <= 4800;"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "Ez-i12QiK3iG"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17700\n",
            "2 simplex iterations\n",
            "0 barrier iterations\n",
            "x = ({'logic': 650.0, 'memory': 1100.0})\n",
            "optimal value = 17700.00\n"
          ]
        }
      ],
      "source": [
        "chips = [\"logic\", \"memory\"]\n",
        "profits = {\"logic\": 12, \"memory\": 9}\n",
        "copper = {\"logic\": 4, \"memory\": 2}\n",
        "\n",
        "ampl.set[\"CHIPS\"] = chips\n",
        "ampl.param[\"profits\"] = profits\n",
        "ampl.param[\"copper\"] = copper\n",
        "\n",
        "ampl.option[\"solver\"] = SOLVER_MILP\n",
        "ampl.solve()\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "cv00HnWxK3iH"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The dual variable corresponding to:\n",
            "\n",
            "- the constraint on Copper is equal to  3/2\n",
            "- the constraint on Germanium is equal to  0\n",
            "- the constraint on Plastic is equal to  6\n",
            "- the constraint on Silicon is equal to  0\n"
          ]
        }
      ],
      "source": [
        "def ShowDuals(ampl):\n",
        "    import fractions\n",
        "\n",
        "    # display all duals\n",
        "    print(\"The dual variable corresponding to:\\n\")\n",
        "    for name, con in ampl.get_constraints():\n",
        "        print(\n",
        "            \"- the constraint on\",\n",
        "            name,\n",
        "            \"is equal to \",\n",
        "            str(fractions.Fraction(con.dual())),\n",
        "        )\n",
        "\n",
        "\n",
        "ShowDuals(ampl)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mlFIYk5KK3iH"
      },
      "source": [
        "## Robust BIM production planning models\n",
        "\n",
        "Suppose now that there is uncertainty affecting the microchip production at BIM. Specifically, the company notices that the amount of copper needed for the two types of microchips is not _exactly_ 4 and 2 gr, but varies due to some external factors affecting the production process. How does this uncertainty affect the optimal production plan?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To get a feeling for what happens, let us first perform some simulations and data analysis on them. We start by simulating a sample of $n=2000$ observed copper consumption pairs for the production of `f` logic chips and `g` memory chips. The amounts vary around the original values, 4 gr and 2 gr, respectively, according to two independent lognormal distributions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "5ppnDDbMK3iH"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.rcParams.update({\"font.size\": 12})\n",
        "\n",
        "seed = 0\n",
        "rng = np.random.default_rng(seed)\n",
        "n = 2000\n",
        "\n",
        "f = rng.lognormal(np.log(4.0), 0.005, n)\n",
        "g = rng.lognormal(np.log(2.0), 0.005, n)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(f, g, \".\")\n",
        "plt.xlabel(\"Copper gr needed for logic chips\")\n",
        "plt.ylabel(\"Copper gr needed for memory chips\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MO6fztcFK3iI"
      },
      "source": [
        "### Box uncertainty for copper consumption\n",
        "\n",
        "A very simple and somehow naive uncertainty set can be the minimal box that contains all the simulated data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "executionInfo": {
          "elapsed": 21,
          "status": "ok",
          "timestamp": 1633441687195,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "-YUKJpXWK3iI",
        "outputId": "6ffff6df-de4f-4355-9bba-86e5755e7cfd"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Lower bounds {'logic': 3.922766922829344, 'memory': 1.9701110863753781}\n",
            "Upper bounds {'logic': 4.061793174956137, 'memory': 2.0328386701386703}\n"
          ]
        }
      ],
      "source": [
        "plt.figure()\n",
        "plt.plot(f, g, \".\")\n",
        "currentAxis = plt.gca()\n",
        "currentAxis.add_patch(\n",
        "    patches.Rectangle(\n",
        "        (min(f), min(g)),\n",
        "        max(f) - min(f),\n",
        "        max(g) - min(g),\n",
        "        fill=False,\n",
        "        color=\"r\",\n",
        "    )\n",
        ")\n",
        "plt.xlabel(\"Copper gr needed for logic chips\")\n",
        "plt.ylabel(\"Copper gr needed for memory chips\")\n",
        "plt.show()\n",
        "\n",
        "# calculate the upper and lower bounds for each uncertain parameter\n",
        "lower = {\"logic\": min(f), \"memory\": min(g)}\n",
        "upper = {\"logic\": max(f), \"memory\": max(g)}\n",
        "print(\"Lower bounds\", lower)\n",
        "print(\"Upper bounds\", upper)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x-r6VhudK3iI"
      },
      "source": [
        "Using this empirical box uncertainty set, we can consider the following robust variant of their optimization model:\n",
        "\n",
        "$$\n",
        "\\begin{array}{rrcrcl}\n",
        "\\max    &  12 x_1 & + &   9 x_2               \\\\\n",
        "\\text{s.t.}    &     x_1 &   &         & \\leq & 1000 \\\\\n",
        "        &         &   &     x_2 & \\leq & 1500 \\\\\n",
        "        &     x_1 & + &     x_2 & \\leq & 1750 \\\\\n",
        "        & z_1 x_1 & + & z_2 x_2 & \\leq & 4800 & \\forall \\ell \\leq a \\leq u \\\\\n",
        "        &     x_1 & , &     x_2 & \\geq & 0    \\\\\n",
        "\\end{array}\n",
        "$$\n",
        "\n",
        "The above model has an infinite number of constraints, one for every realization of the uncertain coefficients $z$. However, using linear duality, we can deal with this and obtain a robustified LP that we can solve. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Robust counterpart of box uncertainty\n",
        "\n",
        "The first thing to notice is that the copper consumption is modeled by constraints that are equivalent to bounding the following optimization problem:\n",
        "    \n",
        "$$\n",
        "\\begin{array}{rrr}\n",
        "\\max    & x_1 z_1 + x_2 z_2 & \\leq 4800 \\\\\n",
        "\\text{s.t.}    & \\ell \\leq z \\leq u \n",
        "\\end{array}\n",
        "$$\n",
        "\n",
        "or\n",
        "\n",
        "$$\n",
        "\\begin{array}{rrr}\n",
        "\\max    & x_1 z_1 + x_2 z_2 & \\leq 4800 \\\\\n",
        "\\text{s.t.}    & z \\leq u \\\\\n",
        "        & -z \\leq -\\ell.\n",
        "\\end{array}\n",
        "$$\n",
        "\n",
        "Now we use linear duality to realize that the above is equivalent to:\n",
        " \n",
        "$$\n",
        "\\begin{array}{rrr}\n",
        "\\min    & u y  - \\ell w & \\leq 4800 \\\\\n",
        "\\text{s.t.}    & y - w = x \\\\\n",
        "        & y \\geq 0, w \\geq 0\n",
        "\\end{array}\n",
        "$$\n",
        "    \n",
        "and the constraint imposed by the last problem is equivalent to:\n",
        "\n",
        "$$\n",
        "\\begin{array}{rrl}\n",
        "   & u y  - \\ell w & \\leq 4800 \\\\\n",
        "   & y - w & = x \\\\\n",
        "   & y \\geq 0, w \\geq 0\n",
        "\\end{array}\n",
        "$$\n",
        "\n",
        "The only thing we need to do is add the new auxiliary variables and constraints to the original model and implement them in AMPL."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Overwriting BIM_robust_box.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile BIM_robust_box.mod\n",
        "\n",
        "set CHIPS;\n",
        "\n",
        "param profits{CHIPS};\n",
        "param copper{CHIPS};\n",
        "\n",
        "var x{CHIPS} >= 0, integer;\n",
        "\n",
        "maximize Profit: sum {c in CHIPS} profits[c] * x[c];\n",
        "\n",
        "s.t. Silicon: x['logic'] <= 1000;\n",
        "s.t. Germanium: x['memory'] <= 1500;\n",
        "s.t. Plastic: sum {c in CHIPS} x[c] <= 1750;\n",
        "\n",
        "param lower{CHIPS};\n",
        "param upper{CHIPS};\n",
        "    \n",
        "var y{CHIPS} >= 0;\n",
        "var w{CHIPS} >= 0;\n",
        "\n",
        "s.t. RobustCopper:\n",
        "    sum {c in CHIPS} (upper[c]*y[c] - lower[c]*w[c]) <= 4800;\n",
        "s.t. PerVariable{c in CHIPS}:\n",
        "    x[c] == y[c] - w[c];\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "KdZk74bBK3iI"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17587.20087\n",
            "2 simplex iterations\n",
            "0 barrier iterations\n",
            "x = ({'logic': 612.4002900543649, 'memory': 1137.599709945635})\n",
            "optimal value = 17587.20\n"
          ]
        }
      ],
      "source": [
        "def BIMWithBoxUncertainty(lower, upper, int_x=False):\n",
        "    ampl = AMPL()\n",
        "    ampl.read(\"BIM_robust_box.mod\")\n",
        "\n",
        "    ampl.set[\"CHIPS\"] = chips\n",
        "    ampl.param[\"profits\"] = profits\n",
        "    ampl.param[\"copper\"] = copper\n",
        "\n",
        "    ampl.param[\"lower\"] = lower\n",
        "    ampl.param[\"upper\"] = upper\n",
        "\n",
        "    if not int_x:\n",
        "        ampl.eval(\"let {i in CHIPS} x[i].relax := 1;\")\n",
        "\n",
        "    ampl.solve(solver=SOLVER_MILP)\n",
        "    assert ampl.solve_result == \"solved\", ampl.solve_result\n",
        "\n",
        "    return ampl\n",
        "\n",
        "\n",
        "ampl = BIMWithBoxUncertainty(lower, upper)\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We may want to impose the box uncertainty set to be symmetric with respect to the nominal values and just choose its width $\\delta$. This leads to a different optimal robust solution."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "executionInfo": {
          "elapsed": 18,
          "status": "ok",
          "timestamp": 1633441687553,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "ZM3Ym0UkK3iI",
        "outputId": "0f195fd9-1969-425f-b843-fb4288d4bc44"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17568.75\n",
            "2 simplex iterations\n",
            "0 barrier iterations\n",
            "x = ({'logic': 606.2499999999999, 'memory': 1143.75})\n",
            "optimal value = 17568.75\n"
          ]
        }
      ],
      "source": [
        "# The parameter delta allows you to tune the amount of uncertainty.\n",
        "# In particular, if you take delta=0, you obtain the same result as the nominal model.\n",
        "delta = 0.05\n",
        "\n",
        "\n",
        "def BIMWithSymmetricalBoxUncertainty(delta, int_x=False):\n",
        "    lower = {chip: copper[chip] - delta for chip in chips}\n",
        "    upper = {chip: copper[chip] + delta for chip in chips}\n",
        "    return BIMWithBoxUncertainty(lower, upper, int_x)\n",
        "\n",
        "\n",
        "ampl = BIMWithSymmetricalBoxUncertainty(delta)\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h4IvEuocK3iJ"
      },
      "source": [
        "### Integer solution variant\n",
        "\n",
        "The original BIM model gave integer solutions, but not the robust version. If we need integer solutions then we should impose that to the nature of the variables, which in this case of _box uncertainty_ is easy to do since the model remains linear, although it will be mixed integer. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "executionInfo": {
          "elapsed": 16,
          "status": "ok",
          "timestamp": 1633441687554,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "lhAQo89qK3iJ",
        "outputId": "43b5ff1a-ade5-4704-e844-8c95a8dc7ba8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17586\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "x = ({'logic': 612.0000000000006, 'memory': 1137.999999999999})\n",
            "optimal value = 17586.00\n"
          ]
        }
      ],
      "source": [
        "ampl = BIMWithBoxUncertainty(lower, upper, True)\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let us see how the optimal solution behave as we vary the width of the box uncertainty set $\\delta$ from 0 to 0.5. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 703
        },
        "executionInfo": {
          "elapsed": 808,
          "status": "ok",
          "timestamp": 1633441688349,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "1aGhPp8XPz4G",
        "outputId": "256b5175-ecc7-45c4-86eb-4925fb9a15a2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17700\n",
            "2 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17634\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17568\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17502\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17436\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17370\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17304\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17238\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17175\n",
            "2 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17109\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17043\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16977\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16911\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16845\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16779\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16713\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16650\n",
            "2 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16584\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16518\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16416\n",
            "3 simplex iterations\n",
            "1 branching nodes\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 16296\n",
            "1 simplex iterations\n",
            "1 branching nodes\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>profit</th>\n",
              "      <th>logic</th>\n",
              "      <th>memory</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0.000</th>\n",
              "      <td>17700.0</td>\n",
              "      <td>650.0</td>\n",
              "      <td>1100.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.025</th>\n",
              "      <td>17634.0</td>\n",
              "      <td>628.0</td>\n",
              "      <td>1122.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.050</th>\n",
              "      <td>17568.0</td>\n",
              "      <td>606.0</td>\n",
              "      <td>1144.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.075</th>\n",
              "      <td>17502.0</td>\n",
              "      <td>584.0</td>\n",
              "      <td>1166.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.100</th>\n",
              "      <td>17436.0</td>\n",
              "      <td>562.0</td>\n",
              "      <td>1188.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.125</th>\n",
              "      <td>17370.0</td>\n",
              "      <td>540.0</td>\n",
              "      <td>1210.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.150</th>\n",
              "      <td>17304.0</td>\n",
              "      <td>518.0</td>\n",
              "      <td>1232.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.175</th>\n",
              "      <td>17238.0</td>\n",
              "      <td>496.0</td>\n",
              "      <td>1254.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.200</th>\n",
              "      <td>17175.0</td>\n",
              "      <td>475.0</td>\n",
              "      <td>1275.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.225</th>\n",
              "      <td>17109.0</td>\n",
              "      <td>453.0</td>\n",
              "      <td>1297.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.250</th>\n",
              "      <td>17043.0</td>\n",
              "      <td>431.0</td>\n",
              "      <td>1319.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.275</th>\n",
              "      <td>16977.0</td>\n",
              "      <td>409.0</td>\n",
              "      <td>1341.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.300</th>\n",
              "      <td>16911.0</td>\n",
              "      <td>387.0</td>\n",
              "      <td>1363.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.325</th>\n",
              "      <td>16845.0</td>\n",
              "      <td>365.0</td>\n",
              "      <td>1385.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.350</th>\n",
              "      <td>16779.0</td>\n",
              "      <td>343.0</td>\n",
              "      <td>1407.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.375</th>\n",
              "      <td>16713.0</td>\n",
              "      <td>321.0</td>\n",
              "      <td>1429.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.400</th>\n",
              "      <td>16650.0</td>\n",
              "      <td>300.0</td>\n",
              "      <td>1450.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.425</th>\n",
              "      <td>16584.0</td>\n",
              "      <td>278.0</td>\n",
              "      <td>1472.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.450</th>\n",
              "      <td>16518.0</td>\n",
              "      <td>256.0</td>\n",
              "      <td>1494.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.475</th>\n",
              "      <td>16416.0</td>\n",
              "      <td>243.0</td>\n",
              "      <td>1500.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0.500</th>\n",
              "      <td>16296.0</td>\n",
              "      <td>233.0</td>\n",
              "      <td>1500.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        profit  logic  memory\n",
              "0.000  17700.0  650.0  1100.0\n",
              "0.025  17634.0  628.0  1122.0\n",
              "0.050  17568.0  606.0  1144.0\n",
              "0.075  17502.0  584.0  1166.0\n",
              "0.100  17436.0  562.0  1188.0\n",
              "0.125  17370.0  540.0  1210.0\n",
              "0.150  17304.0  518.0  1232.0\n",
              "0.175  17238.0  496.0  1254.0\n",
              "0.200  17175.0  475.0  1275.0\n",
              "0.225  17109.0  453.0  1297.0\n",
              "0.250  17043.0  431.0  1319.0\n",
              "0.275  16977.0  409.0  1341.0\n",
              "0.300  16911.0  387.0  1363.0\n",
              "0.325  16845.0  365.0  1385.0\n",
              "0.350  16779.0  343.0  1407.0\n",
              "0.375  16713.0  321.0  1429.0\n",
              "0.400  16650.0  300.0  1450.0\n",
              "0.425  16584.0  278.0  1472.0\n",
              "0.450  16518.0  256.0  1494.0\n",
              "0.475  16416.0  243.0  1500.0\n",
              "0.500  16296.0  233.0  1500.0"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import pandas as pd\n",
        "\n",
        "df = pd.DataFrame()\n",
        "for delta in np.linspace(0, 0.5, 21):\n",
        "    ampl = BIMWithSymmetricalBoxUncertainty(delta, True)\n",
        "    x = ampl.get_variable(\"x\").to_dict()\n",
        "    results = [ampl.get_value(\"Profit\")] + [x[str(i)] for i in chips]\n",
        "    df.at[delta, \"profit\"] = results[0]\n",
        "    df.at[delta, chips[0]] = results[1]\n",
        "    df.at[delta, chips[1]] = results[2]\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can visualize how these quantities change as a function of $\\delta$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "executionInfo": {
          "elapsed": 314,
          "status": "ok",
          "timestamp": 1633441688637,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "LfUxfNz7UcIO",
        "outputId": "937c90d3-d590-4e2d-f73c-91d6cb6df02a"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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zMwwcOLDaW7v79+9H9+7dYW5uDicnJ0yZMgXJyclqfaZPnw4rKyvExMRgxIgRsLa2xvPPP48VK1bAxMSk2jpgoaGhsLOzUyXeRM1KWQmQGAGcXA+EPQWs9QR2jQbObAKSI5WJk4Mv0H06MG4nsDQamHsOGLYGaD+ciRMZPK2SJx8fHxw7dgwAEBkZiejoaAwbNkzVfv/+/Qad75SYmIjs7Gx07twZPj4+8PHxQb9+/QAoyw34+Pjg+vXrAIDAwEAUFhbixo0baseIiIhQtQNAmzZt4OzsjMjISI33u3Dhgqof1d7EiROhUCiwdu1aBAUF4f3338fHH3+M//znP2jTpg3WrVsHf39/LF26FKdOnQKgLGg6atQofPjhh3j66aexefNmjBkzBh999BEmTpyo8R6nT5/Gq6++imnTpmHlypW4ceMGnnrqKXz22Wf49NNPMXfuXLz22msIDw/Hiy++qLZvWFgYJkyYACMjI6xZswazZs3CTz/9hL59+yInJ0etb2lpKYYOHQoXFxd8+OGHePbZZ/HCCy+gtLQUP/zwg1rf4uJiHDhwAM8++6zaPzKIDJZCoSxAefZTYPc4YK0X8PWTwPEPlHOZyooBa1eg6yRgzDbglX+AhVHA058AAc8AVs76PgMi3RK08OmnnwoikUjo0qWLYG9vL3h4eAiFhYWq9pEjRwoDBw7U5tBqLl68KAAQdu7cqbb977//Fn7++We1n+3btwsAhOnTpws///yzkJOTIwiCINy9e1cwMTER5s2bp9pfoVAI/fr1E9q0aSOUlpaqtr/88suCubm5kJiYqNp27NgxAYCwbdu2Wsedm5srABByc3OrbZfJZML169cFmUym3qBQCII8v+n8KBS1PueqVqxYIQAQQkNDVdtKS0sFd3d3QSQSCWvXrlVtz87OFszNzYVp06YJgiAI3377rSAWi4XTp0+rHfPzzz8XAAhnz55VbQMgSCQSIS4uTrWt4nPQunVrQSqVqrYvX75cAKDqW1xcLLi4uAgBAQFqv4dDhw4JAIR33nlHtW3atGkCAOH//u//NM41ODhYCAoKUtv2008/CQCE48eP13iNavwMEDUFCoUgpN0ShIgdgvD984Kw1ksQVtio/6z1FoQfXhCEC18IQvodrf++IGpKHvX9XUGrOU8LFiyAmZkZDh8+jO7du2PZsmWq+UBZWVm4d+8eXn75Za0Tui1btiAnJ0f1JNxvv/2mui23YMECPP7443j88cfV9qm4JdO5c2eMGTNGtd3d3R2vvPIKNmzYgJKSEvTs2RO//PILTp8+jT179qgKZALAG2+8gf3792PQoEFYtGgR8vPzsWHDBnTp0gUzZszQ+nxqraQQWO3W8O9TW2+k1GvBzJdeekn1/0ZGRujRoweSkpIwc+ZM1XY7Ozu0b98esbGxAJS30Tp27IgOHTogI6Oy1ssTTzwBADh+/DhCQkJU2wcPHgxvb2/V66CgIADAs88+C2tra43tsbGx8Pb2RmRkJNLS0rBy5Uq10aGRI0eiQ4cO+P333zWeoJwzZ47GOU6dOhVz5sxBTEwM/Pz8AAB79uyBh4cHBgwYUMsrRdQE5CRWzlmKOwXk31NvN7UCvPpUzlty6QyIm9wKX0SNQus6T7NmzcKsWbM0tjs4OFR766suPvzwQyQkJKhe//TTT/jpp58AQDWHpi7Wrl0Le3t7bN++HWFhYWjbti12796NyZMnq/Xz8PDAyZMnsWTJEvzf//0fTE1NMXLkSGzcuJHznbRQtdgoANja2sLMzAxOTk4a2zMzMwEAd+7cwY0bN+DsXP0wf1pa2iPfA4DGgwQV27OzswFA9flq3769xnt06NABZ86cUdtmbGwMd3d3jb4TJ07EK6+8gj179uCdd95Bbm4uDh06hMWLF9dYe4yoSchPK0+UyhOm7Hj1diMJ4BlUXmtpAOAWyPIBROXqVSSzrKwMf//9t2rUx9vbG927d1cbzdFGTTWbHsbb21tjUngFsViM5cuXY/ny5Y88TufOnfHnn3/W+f11wsRCOdrTVJjU79Hh6j4HNX02Kn53CoUCXbp0waZNm6rt92BSVNPxHvU+dSWRSCCu5l/Z9vb2eOqpp1TJ04EDByCXyzFlyhSt3oeowchygPgzlSNL6erzQCEyAtx7VJYPcO8FmHDOHlF1tE6ewsLCsHz5cqSlpam+kEQiEZydnbF69WqNyblUCyJRvW6TNQd+fn64cuUKBg8e3KAjN15eXgCAW7duqW4JVrh165aqvTamTp2K0aNH4+LFi9izZw+6deuGzp076zReojorLgASwyuTpdQrgKCo0kGkrNzt0185suQVDEisazwcEVXSKnnavn075syZg8DAQKxcuRLt2rUDoPzS2b59O2bNmoXi4uJ6zXuilmnChAk4fPgwvvjiC421BGUyGRQKhU7qK/Xo0QMuLi74/PPP8eKLL6puy/7xxx+4ceNGtesk1mT48OFwcnLCunXrcPLkSWzYsKHe8RHVWWkxkHSxMllKuggoStT7OLWrHFny7gdYOOgnViIDp1XytG7dOvTr1w/Hjh2DiUnlPfBBgwZh5syZeOKJJ7B+/XomT1RnL7zwAvbt24eXX34Zx48fR58+fVBWVoabN29i3759+PPPP6tdf7CuTExMsG7dOsyYMQMDBgzAc889h/v37+OTTz6Bt7c3Fi9eXKdjTZo0CVu2bIGRkRGee+65esdH9EiKMiD1cmWylBAOlMrU+9h6VK4P59MfsNFcfoqI6k6r5OnevXt49dVX1RKnChVfJK+//nq9g6OWRywW45dffsFHH32EXbt24eeff4aFhQV8fX2xaNEi1SinLkyfPh0WFhZYu3Ytli1bBktLS4wdOxbr1q2DnZ1dnY41depUbNmyBYMHD652fUSiehMEIO1GZbIUfwaQ56r3sXSuTJR8BgD23srpAESkUyJBixm0ffr0QY8ePfDJJ59U275o0SJERkbi7Nmz9Q7QEEmlUtja2iI3Nxc2NjYa7UVFRYiLi4OPjw+LKDYTV65cQWBgIHbt2oUXXnjhkf35GaBHEgQgO06ZKMWeVBajLHigmr3EFvDuW5kwuXRkskRUD4/6/q6g1cjT5s2bMXLkSPj6+iI0NFRV40kmk+Hzzz/Hvn37cPjwYe0iJzJAX3zxBaysrPDMM8/oOxQyZNIUIO50ZfmA3Lvq7cbmyondFcmSayAgrt/TzURUd1olT9OnT4eRkRGWLFmC119/XbU+XEpKCkpLS+Hm5qa2cDCgfBLvypUr9Y+YqAn57bffcP36dezYsQPz58/nYsFUN4VZyhGliuKUmXfU28UmgHvPKuUDegDGrDlHpG9aJU8ODg5wdHRE27Zt1bZXrfRM1BIsWLAA9+/fx4gRIzQqkhNpkOcpJ3bHnVT+3PsHQNWZEyJlMcqKZMkzuMWXLyFqirRKnk6cOKHjMIgMkzYFXakFKSkCki5Ujiwl/w0IZep9nDtWKR/QBzC310+sRFRr9aowTkREVZSVAilRQNwJZbKUGAGUydX72HtXPg3n3Q+wbqWPSImoHmqVPJ06dQoA0L9/f7XXj1LRn4ioWVIogLR/K5+ISzgHFOep97FqXaV8QH/AvvbV64moaapV8jRw4ECIRCLIZDKYmpqqXtdEEASIRCKUlZXV2Ie0X2eNDB9/9wZKEIDMmMo5S3GnAVmWeh8zO8CnX+WCuk5tWT6AqJmpVfJ0/PhxAICpqanaa9JORXHRwsJCVZkHalkKCwsBoNpCs9TE5CZVzlmKOwXkPbB4t4kl4BUC+JZX8m7VBahmEWkiaj5qlTwNGDDgoa+pboyMjGBnZ4e0tDQAgIWFRYMugktNhyAIKCwsRFpaGuzs7GBkxBo9TU5+OhB/qjJZyopVbzcyBTyCKpc9afM4YMQkmKgl4YRxPWndujUAqBIoalns7OxUnwHSs6JcIP5sZbKU9q96u8hImSBVzFnyCAJMOGJM1JJpnTzduHEDO3fuRGxsLLKzszXmcIhEIvz111/1DrC5EolEcHV1hYuLC0pKSh69AzUbJiYmHHHSp+JC4O75ymQpJQoQFOp9WgVUjix5BQNmtvqJlYiaJK2Sp2+//RYzZsyAiYkJ2rdvD3t7zboknBBbO0ZGRvwiJWpIpcXK+koVyVLSBaCsWL2Pg1/lnCXvfoClk35iJSKDoNXCwH5+fnBwcMAff/wBJyf+JfOg2i4sSEQNQFEG3LtamSwlhAMlBep9bNpUjiz59ANs3fUTKxE1KQ26MHBKSgqWLl3KxImI9E8QgPRb5cnSSeVacUW56n0sHKvUWhoAOPiyfAARaU2r5Klr165ISUl5dEciooaQHV85shR3Csi/r95uaq1c6qRidMmlE8sHEJHOaJU8bdq0CePHj8fw4cMREhKi65iIiNTl3VMWpIwrr7eUk6DebmwGePauHFlyDQSM+DAxETWMWv3tMmrUKI1ttra26NevHzp16gRPT0+NSc8ikQgHDx7UTZRE1LIUZgEJVcoHpN9UbxcbA216VN6Kc+8JmJjpJ1YianFqlTxdvXq12iKOnp6eyM/Px/Xr1zXaWPSRiGpNng8knq8cWUq9AqDqsywiwLVr5ciSZ29AYq2vaImohatV8hQfH9/AYRBRi1IiA5IuAvFnyssHXAQUpep9nNpXjix59wUsHPQTKxHRAzgpgIgaXnEBcPeC8lZc/Bll3aUHay3ZegK+5SNL3v0AG1f9xEpE9AhaJU9Hjx7F8ePHsXr16mrb33zzTQwePBhPPPFEvYIjIgMlz1dW8Y4/o1z6JOWS5siStSvg1adydMnem+UDiMggaJU8vf/++/D09KyxPTk5Ge+//z6TJ6KWokiqnLMUf1o5upRyGRDK1PvYuCvLB3j3VSZNrLVERAZKq+Tp2rVrGD9+fI3tPXv2xKFDh7QOioiaOFm2snJ3xW24e1c114ez8wS8+iqTJe8+gJ0XkyUiaha0Sp7kcjmKi4sf2l5YWKh1UETUxFSUDog/CyScAe79A/Wn4QDY+5QnSuUjS3YeegmViKihabW2XVBQEExNTXH69GmNNkEQ0K9fPxQVFSEyMlInQRoarm1HBq8oF0g4V1ln6f4/mn0c2ypHlLzKR5Zs3Bo/TiIiHWrQte0WLFiAqVOnYvz48XjnnXfQsWNHAMD169fx7rvvIjw8HF9//bV2kRNR4ysuBO5GVK4PlxKleRvOuYNyRMm7j/K/1q31EysRkZ5plTxNmTIFMTExeO+99/DTTz9BXL5mlEKhgEgkwltvvYVp06bpNFAi0qGyEmW5gLhTQOxJIOmCZukAB78qdZb6AVbO+omViKiJ0eq2XYWYmBj8/PPPiI2NBQD4+flhzJgx8PPz01mAhoi37ajJUZQB965VjiwlhAMlBep9rN0A3wGVCZOtu35iJSLSk9p+f9creaLqMXkivRMEION2+cjSCeUTcUU56n0sHJUjSj79Ad+BLB1ARC1eg855IqImKDuhcoJ33Ckg/556u6m1cr5SxfpwLp2A8lvuRERUe0yeiAxV3n1lUcrYE8pkKSdBvd3YDPAIqkyW3LoBRvwjT0RUX/yblMhQyLKVdZbiTiqTpfSb6u0iI8C9R+WcJfdegImZfmIlImrGmDwRNVXFBUBiuPJpuLhTQOoVqBemFAGtu1QmS14hgMRaX9ESEbUYTJ6ImopSOZAUWTmylBQJKErU+zi1Uy8fYOGgn1iJiFqwJjVbND8/HytWrMCwYcPg4OAAkUiEsLAwtT4KhQJhYWEYNWoUPDw8YGlpiYCAALz//vsoKiqq9rhfffUVOnbsCDMzM7Rt2xabN2+utl9ycjImTJgAOzs72NjYYPTo0aoyDEQ6pyhT1lo68xGwawyw1gsIGwGcXKcccVKUALYeQOAUYOwOYMlNYP5FYORGoNNoJk5ERHpSq5GnJ554os4HFolE+Ouvv+q0T0ZGBt599114enrisccew4kTJzT6FBYWYsaMGejduzdefvlluLi4IDw8HCtWrMBff/2F//3vfxBVedx6+/btePnll/Hss89iyZIlOH36NBYuXIjCwkIsW7ZM1S8/Px+DBg1Cbm4u3njjDZiYmOCjjz7CgAEDcPnyZTg6Otb5GhCpEQQg7UZlraX4s4A8V72PpXPlBG+f/oC9N8sHEBE1MbVKnioqh1d19+5dxMbGwtbWFr6+vgCAuLg45OTkwM/PDx4edV8U1NXVFampqWjdujUiIyPRs2dPjT6mpqY4e/YsQkJCVNtmzZoFb29vVQI1ZMgQAIBMJsObb76JkSNH4sCBA6q+CoUC7733HkJDQ2Fvbw8A2Lp1K+7cuYMLFy6o3nf48OEICAjAxo0bsXr16jqfD7VwggBkx1VW8Y4/DRSkq/eR2CoX0q0oTuncgckSEVETV6vk6cERoDNnzmDUqFH44osvMG3aNBgbKw9TWlqKnTt3YtmyZRq322pDIpGgdeuHr5dlamqqljhVGDt2LFasWIEbN26okqfjx48jMzMTc+fOVes7b9487NmzB7///jumTJkCADhw4AB69uyplrB16NABgwcPxr59+5g8Ue1IU9RrLeXeVW83Nge8gitHllwfA8RG+omViIi0otWE8aVLl2LGjBmYOXOm+sGMjTFr1izcvHkTS5YsQUREhE6CrI1795QFAZ2cnFTboqKiAAA9evRQ69u9e3eIxWJERUVhypQpUCgUuHr1Kl588UWN4/bq1QtHjhxBXl4erK2rf5JJLpdDLperXkul0nqfDxmIwiz1ZCnzjnq72ARw71k5stSmB2Bsqp9YiYhIJ7RKnq5evYoXXnihxnYfHx9s27ZN66C0sX79etjY2GD48OGqbampqTAyMoKLi4taX1NTUzg6OiIlJQUAkJWVBblcDldXV43jVmxLSUlB+/btq33vNWvWYNWqVbo6FWrKiqTKydwV85buXVNvF4mVo0kVI0uevQFTS/3ESkREDUKr5MnNzQ0//PADZs+erbplV6G0tBQ//PAD3NzcdBJgbaxevRrHjh3D1q1bYWdnp9ouk8lgalr9v/LNzMwgk8lU/QDlbcPq+lXtU53ly5djyZIlqtdSqVSrOV/UBJXIgLsXKkeWkv8GhDL1Ps4dK0eWvEIAc3v9xEpERI1Cq+Tp9ddfx8svv6x64s3f3x8AcOfOHXz++ee4fPkytm7dqtNAa/LDDz/grbfewsyZMzFnzhy1NnNzcxQXF1e7X1FREczNzVX9AKjdeqvar2qf6kgkkmoTLzJAZSVASpRyVCn2pDJxKnvgc2HvXTmy5NMfsHKp9lBERNQ8aZU8hYaGwsjICG+++SZCQ0NVT+IJggBnZ2d8/vnnmDVrlk4Drc7Ro0cxdepUjBw5Ep9//rlGu6urK8rKypCWlqZ26664uBiZmZmq0TEHBwdIJBKkpqZqHKNiW2OOpFEjUiiA+/9U3oZLOAcU56v3sWpdObLk3Q+w99JPrERE1CRoXWF85syZmDZtGi5evIjExEQAgJeXF3r06KFxK68hREREYOzYsejRowf27dtX7XsGBgYCACIjIzFixAjV9sjISCgUClW7WCxGly5dEBkZWe37+Pr61jhZnAyMIACZ0ZVVvONOA7Is9T5mdoBPv/LRpQGAU1uWDyAiIpV6ZTnGxsYIDg5GcHCwruKplRs3bmDkyJHw9vbGoUOHaryl9sQTT8DBwQHbtm1TS562bdsGCwsLjBw5UrVt3Lhx+L//+z9ERkaqns67desW/ve//2Hp0qUNe0LUsHLuqj8Rl5ei3m5qpZyrVHEbrlUXQNykiu8TEVETIhIEQXh0N01SqRRbt27F8ePHkZaWhu3bt6NXr17IyspSLZ9SMReqLrZs2YKcnBykpKRg27ZteOaZZ9CtWzcAwIIFCyAWi9G5c2ckJydj9erVaNOmjdr+fn5+asnc1q1bMW/ePIwbNw5Dhw7F6dOnsWvXLnzwwQd44403VP3y8vLQrVs35OXlYenSpTAxMcGmTZtQVlaGy5cvw9nZuU7XxtbWFrm5ubCxsanzNaB6yk8H4k9VFqfMjlNvN5IAHr0q5y21eRwwMtFPrERE1GTU9vtbq+QpKSkJAwYMwN27d9G2bVvcvHkTR48eVS3j0r59ewwbNgyffPJJnQP39vZGQkJCtW1xccovQR8fnxr3nzZtmkaBzi+++AIbN25EXFwcPDw8MH/+fCxatEijanpSUhIWL16MI0eOQKFQYODAgfjoo4/qnAQyeWpkshzlXKWKeUtp19XbRUbKBKliZMkjCDCp+QEAIiJqmWr7/a3VbbvXXnsNeXl5uHz5MlxcXDTqKI0ZMwaHDh3S5tCIj49/ZJ+65nuzZs2q1QR2d3d37N+/v07HJj0oLgTunq+8DZcSBQgK9T6tulQmS14hgBmTWCIi0g2tkqcjR45g8eLF6NSpEzIzMzXafX19cffu3Wr2JNJCabGyvlJFspR0ASh7oASFo3/lgrre/QBLLuRMREQNQ6vkSSaTPXQOUF5entYBEUFRBty7WpksJYQDJQXqfWzaKBMl3/JkybZN9cciIiLSMa2Sp06dOuHUqVOYPXt2te2//PKLapI30SMJApB+q3LOUvwZoChHvY+FY+XIkk9/wMGX5QOIiEgvtEqeXnnlFUybNg1du3bF+PHjAQAKhQLR0dFYtWoVwsPD8eOPP+o0UGpmsuPVywfk31dvl9gAXn0qi1M6d2T5ACIiahK0LlXwwQcfYOXKlRAEAQqFAmKxGIIgQCwW4/3338eyZct0HavB4NN21ci7pyxIWVGcMueBJyqNzZSL6Pr0B3wGKhfXNWr4YqtEREQVGrRUQYXExET8+OOPiI6OhkKhgJ+fH5555hn4+vpqe8hmgckTgMIsIOFs5chS+k31drEx0KaHMlnyHQC49wSMuT4gERHpT6MkT1S9Fpk8yfOBxPOVI0upVwBU/WiJANeulSNLnr0BiZV+YiUiIqpGg9Z5unTpEs6fP4+5c+dW275161aEhISo1o6jZqhUDiRdrKzinRwJKErV+zi1r6y15N0XsHDQT6xEREQ6pNXI0/Dhw2Fubo6ffvqp2vZx48ahqKhI60KZhq5ZjjyVlSpHk+JOKn8SI4BSmXofW0/At3xkyacfYN1aH5ESERFppUFHnv7++28sX768xvZ+/fphzZo12hyamgqFAki/UTmylHAWkEvV+1i6VM5Z8ukP2HvrJVQiIqLGpFXylJeXB2PjmncVi8XIzc3VOijSA0EAsmIray3FnQYKM9T7mNkqC1JW1Fpybs9aS0RE1OJolTy1bdsWR44cwYIFC6pt/+9//9vin7gzCLnJQPxp5chS3ClAmqTebmKhXBeuYt5S666A2Eg/sRIRETURWiVPM2fOxOLFi7FkyRK88847sLOzAwDk5ORg1apV+O9//4sNGzboMk7ShYJMZbJU8URcZrR6u5Ep4N6rMllq0x0wNtVPrERERE2UVhPGBUHAiy++iG+++QZisRhubm4AgJSUFCgUCrzwwgsICwuDqIXe0mkyE8aLpEBieOXI0v1r6u0iMeDWrTJZ8ugNmFroJ1YiIiI9a5Q6T8ePH8ePP/6I2NhYAICfnx+effZZDBw4UNtDNgt6S55KZMDdC5UjS8mXAKFMvY9L58pkySsEMLdrvPiIiIiaMBbJ1KNGS57KSoCUqPKRpZPKxKlMrt7HwbdKraV+gJVLw8VDRERkwBq0VAHpiUIB3P+n8om4hHNAcb56H2vXyqfhfPoBdp76iZWIiKiZ0ip58vHxeeR8JpFIhJiYGK2ComoUZABbegKyLPXt5g7KJMmnvzJpcvRn+QAiIqIGpFXyNGDAAI3kqaysDAkJCTh79iwCAgLQrVs3nQRI5SwcAVMroKwY8OpTeSuuVQAgFus7OiIiohZDq+QpLCysxrYrV65g6NCheP7557WNiaojEgHTfgVs3QEjE31HQ0RE1GLpfMjisccew+zZs7Fs2TJdH5ocfJg4ERER6VmD3O9p1aoVrl+/3hCHJiIiItIrnSdPmZmZ+Oqrr+Du7q7rQxMRERHpnVZznp544olqt+fk5ODmzZsoLi7Gt99+W6/AiIiIiJoirZInhUKh8bSdSCSCj48PhgwZghdffBEdOnTQSYBERERETYlWydOJEyd0HAYRERGRYWCBICIiIqI6qNXI065du7Q6+NSpU7Xaj4iIiKipqtXCwOJqKlhXzHl6cPeqc6HKysrqG59BarSFgYmIiEhndLowcFxcnNrrnJwcTJs2Dba2tliwYAHat28PALh58yY2b96MvLw8fPPNN/UIn4iIiKhpqtXI04NmzJiBpKQkHDlyROOpO4VCgSeffBIeHh7YuXOnzgI1JBx5IiIiMjy1/f7WasL4L7/8grFjx2okToDyFt8zzzyDgwcPanNoIiIioiZNq+RJEATcvHmzxvbr169rzIUiIiIiag60Sp7GjBmDbdu2YdOmTSgsLFRtLywsxMaNG7F9+3aMHj1aZ0ESERERNRVazXnKzc3FqFGjcPr0aZiYmMDV1RUAkJqaipKSEvTp0we//fYb7OzsdB2vQeCcJyIiIsNT2+9vrZKnCgcPHsThw4eRmJgIAPDy8sKIESPw9NNPVzsfqqVg8kRERGR4GiV5ouoxeSIiIjI8Oq3zVJOCggKcPHkSCQkJAABvb2/0798flpaW9TksERERUZOldfK0efNmvPXWW8jPz1d7ss7a2hoffPAB5s+fr5MAiYiIiJoSrZ6227VrFxYtWoSAgAB89913uHz5Mi5fvoy9e/eiS5cuWLRoEb799lutAsrPz8eKFSswbNgwODg4QCQSISwsrNq+N27cwLBhw2BlZQUHBwe88MILSE9P1+inUCiwfv16+Pj4wMzMDF27dsXevXvrdUwiIiJqmbSa8xQYGAg7Ozv89ddfMDIyUmsrKyvD4MGDkZOTg8uXL9c5oPj4ePj4+MDT0xO+vr44ceIEdu7cienTp6v1S0pKQrdu3WBra4uFCxciPz8fH374ITw9PXHhwgWYmpqq+i5fvhxr167FrFmz0LNnTxw8eBC///479u7di0mTJml1zIfhnCciIiLDU+vvb0ELZmZmwpYtW2ps37Jli2BmZqbNoYWioiIhNTVVEARBuHjxogBA2Llzp0a/OXPmCObm5kJCQoJq29GjRwUAwvbt21XbkpKSBBMTE2HevHmqbQqFQujXr5/g7u4ulJaW1vmYj5KbmysAEHJzc2u9DxEREelXbb+/tbptZ2tri/j4+Brb4+PjtR5xkUgkaN269SP7/fjjj3jqqafg6emp2jZkyBC0a9cO+/btU207ePAgSkpKMHfuXNU2kUiEOXPmICkpCeHh4XU+JhEREbVcWiVPI0eOxObNm/H9999rtP3www/YsmULnn766XoHV5Pk5GSkpaWhR48eGm29evVCVFSU6nVUVBQsLS3RsWNHjX4V7XU9JhEREbVcWj1tt3btWoSHh+P555/Hq6++irZt2wIA7ty5g3v37qFDhw5Yu3atTgOtKjU1FQBUlc2rcnV1RVZWFuRyOSQSCVJTU9GqVSuNop0V+6akpNT5mA+Sy+WQy+Wq11KpVMszIyIioqZOq5EnZ2dnXLp0CZs2bUKXLl1w//593L9/H126dMFHH32Ev//+G05OTrqOVUUmkwFAtYmMmZmZWh+ZTFbrfrU95oPWrFkDW1tb1Y+Hh0edzoeIiIgMR51HnmQyGd58800MGjQIixYtwqJFixoirocyNzcHALXRngpFRUVqfczNzWvdr7bHfNDy5cuxZMkS1WupVMoEioiIqJmq88iTubk5tm/fjvv37zdEPLVSdSHiB6WmpsLBwUE1guTq6op79+6pFfKsuq+bm1udj/kgiUQCGxsbtR8iIiJqnrS6bde9e3f8888/uo6l1tq0aQNnZ2dERkZqtF24cAGBgYGq14GBgSgsLMSNGzfU+kVERKja63pMIiIiarm0Sp4+/vhjfP/99/jyyy9RWlqq65hq5dlnn8WhQ4dw9+5d1ba//voLt2/fxvjx41XbRo8eDRMTE2zdulW1TRAEfP7552jTpg1CQkLqfEwiIiJqubSqMN61a1dkZGTg/v37kEgkaNOmjcZ8IJFIhCtXrmgV1JYtW5CTk4OUlBRs27YNzzzzDLp16wYAWLBgAWxtbXH37l1069YNdnZ2WLRoEfLz87Fhwwa4u7vj4sWLarfYXn/9dWzYsAGhoaHo2bMnfvnlF/z+++/Ys2cPJk+erOpXl2M+DCuMExERGZ7afn9rlTwNHDhQ49H/6hw/fryuhwYAeHt7IyEhodq2uLg4eHt7AwD+/fdfLFmyBGfOnIGpqSlGjhyJjRs3olWrVmr7KBQKrFu3Dtu3b0dqairatm2L5cuX4/nnn9c4fm2P+TBMnoiIiAxPgyZP9HBMnoiIiAxPbb+/tZrzRERERNRSaVVhHFDWQ/riiy9w+PBh1Tp33t7eGDFiBF566SVVYUkiIiKi5kSrkaekpCQEBgZi4cKFuHLlCpydneHs7IwrV65g4cKFCAwMRFJSkq5jJSIiItI7rZKnefPmISEhAfv27UNycjJOnjyJkydPIjk5GT/88AMSExMxb948XcdKREREpHda3bb766+/sHjxYowbN06jbfz48bh06RI2b95c7+CIiIiImhqtRp6sra3h4uJSY3vr1q1hbW2tdVBERERETZVWydOMGTMQFhaGwsJCjbb8/Hzs3LkTM2fOrHdwRERERE2NVrftAgMD8fvvv6NDhw6YNm0a/P39AQB37tzBrl274ODggK5du+Knn35S2++ZZ56pf8REREREeqRVkUyx+NEDViKRCFUPLRKJUFZWVte3MkgskklERGR4avv9rdXIk7bLrhAREREZOq2SpwEDBug6DiIiIiKDwOVZiIiIiOqAyRMRERFRHTB5IiIiIqoDJk9EREREdVCr5OnXX39FSkpKQ8dCRERE1OTVKnkaO3YsTpw4oXrt6+uLX3/9taFiIiIiImqyapU8WVtbIycnR/U6Pj4e+fn5DRUTERERUZNVqzpPvXr1wgcffID79+/D1tYWAHD48GHcu3evxn1EIhEWL16smyiJiIiImohaLc8SHR2NqVOn4vz588qdHlh6pdoDt6DlWB7E5VmIiIgMj06XZ/H398e5c+dQVFSEtLQ0eHt74+OPP8bo0aN1FjARERGRIajT8ixmZmbw9PTEihUr8MQTT8DLy6uh4iIiIiJqkmp12+5h8vPzcffuXQCAh4cHrKysdBKYIeNtOyIiIsNT2+9vrYtkXrx4EYMGDYK9vT0CAgIQEBAAe3t7PPHEE4iMjNT2sERERERNWp1u21WIiIjAwIEDYWpqipdeegkdO3YEANy4cQN79+5F//79ceLECfTq1UunwRIRERHpm1a37YYMGYL4+HicOXMGrVu3Vmu7f/8++vTpAx8fHxw9elRngRoS3rYjIiIyPA162y4iIgKzZ8/WSJwAoFWrVggNDVWVNSAiIiJqTrRKnsRiMUpLS2tsLysrg1jMNYeJiIio+dEqwwkJCcFnn32GhIQEjbbExERs3boVffr0qXdwRERERE2NVnOeoqKi0L9/f5SWlmLs2LFo164dAODWrVs4ePAgjI2Ncfr0aTz22GM6D9gQcM4TERGR4dFphfEHdevWDREREXjzzTfx66+/orCwEABgYWGBYcOG4f3330enTp20i5yIiIioCat3kUyFQoH09HQAgLOzM+c6gSNPREREhqhBR56qEovFaNWqVX0PQ0RERGQQOExEREREVAdMnoiIiIjqgMkTERERUR0weSIiIiKqgzonT4WFhXjmmWewZ8+ehoiHiIiIqEmrc/JkYWGBY8eOqWo7EREREbUkWt2269u3L8LDw3UdS53cuXMHkyZNgru7OywsLNChQwe8++67GknduXPn0LdvX1hYWKB169ZYuHAh8vPzNY4nl8uxbNkyuLm5wdzcHEFBQTh69GhjnQ4REREZCK2Spy1btuD06dN46623kJSUpOuYHunu3bvo1asXzp8/j/nz5+Pjjz9GcHAwVqxYgeeee07V7/Llyxg8eDAKCwuxadMmvPTSS9ixYwfGjx+vcczp06dj06ZNeP755/HJJ5/AyMgII0aMwJkzZxrz1IiIiKiJ06rCuLW1NUpLS1FcXAwAMDY2hkQiUT+wSITc3FzdRPmA1atX480338Q///yDzp07q7ZPmzYNu3btQlZWFuzt7TFixAhcvnwZN2/eVFUK/fLLLzFr1iz8+eefePLJJwEAFy5cQFBQEDZs2IClS5cCAIqKihAQEAAXFxecO3euTvGxwjgREZHhadAK488++yxEIpHWwdWXVCoFAI3K5q6urhCLxTA1NYVUKsXRo0exePFitQswdepULF68GPv27VMlTwcOHICRkRFCQ0NV/czMzDBz5ky88cYbuHv3Ljw8PBrhzIiIiKip0yp5CgsL03EYdTNw4ECsW7cOM2fOxKpVq+Do6Ihz585h27ZtWLhwISwtLXH27FmUlpaiR48eavuampoiMDAQUVFRqm1RUVFo166dRpbZq1cvAMrbf0yeiIiICNDB2nb6MGzYMLz33ntYvXo1fv31V9X2N998E++//z4AIDU1FYByNOpBrq6uOH36tOp1ampqjf0AICUl5aHxyOVyyOVy1euKkTEiIiJqfrQukpmYmIiXX34Z7du3h729PU6dOgUAyMjIwMKFC9VGdhqCt7c3+vfvjx07duDHH3/Eiy++iNWrV2PLli0AAJlMBgAac7EA5S25ivaKvjX1q3qsmqxZswa2traqH45SERERNV9ajTxdv34d/fr1g0KhQFBQEKKjo1FaWgoAcHJywpkzZ1BQUICvvvpKp8FW+P777xEaGorbt2/D3d0dAPDMM89AoVBg2bJleO6552Bubg4AaiNCFYqKilTtAGBubl5jv4r2h1m+fDmWLFmiei2VSplAERERNVNajTy9/vrrsLOzw+3bt7F79248+MDeyJEj1W6L6drWrVvRrVs3VeJUYdSoUSgsLERUVJTqllvF7buqUlNT4ebmpnrt6upaYz8Aan2rI5FIYGNjo/ZDREREzZNWydOpU6cwZ84cODs7V/vUnaenJ5KTk+sdXE3u37+PsrIyje0lJSUAgNLSUgQEBMDY2BiRkZFqfYqLi3H58mUEBgaqtgUGBuL27dsac5UiIiJU7URERESAlsmTQqGAhYVFje3p6enVziHSlXbt2iEqKgq3b99W2753716IxWJ07doVtra2GDJkCHbv3o28vDxVn2+//Rb5+flqhTLHjRuHsrIy7NixQ7VNLpdj586dCAoK4i04IiIiUtFqztPjjz+O33//HXPnztVoKy0txffff4/evXvXO7iavPbaa/jjjz/Qr18/zJ8/H46Ojjh06BD++OMPvPTSS6rbbB988AFCQkIwYMAAhIaGIikpCRs3bsSTTz6JYcOGqY4XFBSE8ePHY/ny5UhLS4O/vz+++eYbxMfHN9i8LSIiIjJQghYOHz4siMVi4eWXXxZOnDghiEQi4bvvvhOOHj0qDBo0SDA2NhZOnjypzaFrLSIiQhg+fLjQunVrwcTERGjXrp3wwQcfCCUlJWr9Tp8+LYSEhAhmZmaCs7OzMG/ePEEqlWocTyaTCUuXLhVat24tSCQSoWfPnsJ///tfrWLLzc0VAAi5ubla7U9ERESNr7bf31otzwIob38tWrQIubm5EAQBIpEIgiDAxsYG27ZtU1tjrqXh8ixERESGp7bf31onTwBQUFCAI0eOIDo6GgqFAn5+fhg6dCisra21PWSzwOSJiIjI8DTo2nYVLC0tMXbs2PocgoiIiMig1Ct5OnToEA4fPoz4+HgAyqrfI0aMwFNPPaWL2IiIiIiaHK1u2+Xk5GDs2LE4deoUjIyM1ApSlpWVoV+/fvjll19gZ2en63gNAm/bERERGZ7afn9rVedp0aJFOH36NNatW4fs7GwkJCQgISEB2dnZWLt2Lc6cOYNFixZpHTwRERFRU6XVbbtffvkFc+fOxdKlS9W2W1pa4rXXXkNiYiJ27dqlkwCJiIiImhKtRp5MTEzQvn37Gts7dOgAExMTrYMiIiIiaqq0Sp6effZZ7N+/v9r15UpLS7Fv3z615U+IiIiImota3ba7dOmS2uspU6Zg/vz5CAkJQWhoKPz9/QEAd+7cwY4dO1BcXIznn39e99ESERER6VmtnrYTi8UQiURq26ruVtH24LbqRqZaAj5tR0REZHh0WiRz586dOguMiIiIyJDVKnmaNm1aQ8dBREREZBC0mjBORERE1FJpvTxLQkICvvnmG8TGxiI7OxsPTp0SiUQ4ePBgvQMkIiIiakq0Sp727t2LadOmobS0FHZ2drC1tdXo8+AEcyIiIqLmQKvkafny5ejQoQMOHDiAdu3a6TomIiIioiZLqzlPGRkZePnll5k4ERERUYujVfIUFBSExMREXcdCRERE1ORplTx9/PHH2L17Nw4cOKDreIiIiIiaNK3mPHXp0gUffPABJk2aBEtLS7i7u8PIyEitj0gkwpUrV3QSJBEREVFToVXytHXrVixYsABmZmbw8/Or9mk7IiIiouaoVmvbPcjd3R0+Pj44dOgQE6dqcG07IiIiw1Pb72+t5jzl5ubi+eefZ+JERERELY5WydOAAQNw7do1XcdCRERE1ORplTxt27YNJ0+exPr165GZmanrmIiIiIiaLK3mPFlbW0OhUKCoqAgAYGZmVu3Tdrm5ubqJ0sBwzhMREZHhqe33t1ZP2z377LNcu46IiIhaJK2Sp7CwMB2HQURERGQYtJrzRERERNRSaTXytGvXrlr1mzp1qjaHJyIiImqytJowLhbXPGBVdS5UWVmZdlEZuIaaMD5rVySsJcYI8XdCiJ8j3OzMdXZsIiKilq5BJ4zHxcVpbCsrK0N8fDy2bt2KxMREfPPNN9ocmmqQKyvBXzfuQyEAP0UlAwC8HS0Q7OeEPv6O6O3rCCcriZ6jJCIiav60Gnl6lJEjR8Lb2xufffaZrg9tEBpi5Km4VIELcVk4F5OBczGZuJqUA8UDv7kOra0R7OeIPn5O6OXrABszE528NxERUUtQ2+/vBkmetm3bhrfffhsZGRm6PrRBaIw6T9KiElyIzcK5mEyci8nAzXt5au1iEdDF3Q59/BwR4ueE7l72MDc1quFoRERE1KC37R4lJiYGcrm8IQ5N5WzMTDCkUysM6dQKAJCZL0d4bCbOxWQiPCYTcRkFuHI3B1fu5mDriRiYGonxuJcdQvyU86Ue87CDiREftiQiIqorrUaeTp06Ve32nJwcnDp1Cp9++inGjBmDffv21TtAQ9QUKoyn5MhUo1LnojNxT1qk1m5haoRePg4IKR+Z6uhqAyMxC58SEVHL1aC37cRicbUVxgVBgJGREcaPH4/NmzfD0dGxroduFppC8lSVIAiIzyxUJVLhsZnIKihW62NrboJgX0eE+DsixM8Rfs5WrCJPREQtSoMmTydPntQ8kEgEe3t7eHl5NYmEQZ+aWvL0IIVCwK37ecqRqegMRMRlIV9eqtbH2VqCkPLJ58F+jvBwsNBTtERERI1DrxPGW7qmnjw9qLRMgavJuQgvv80XGZ8NealCrY+HgzlCfJ0Q4u+IYD9HuFib6SlaIiKihlHb72+DnjF86dIljBo1Cg4ODrCwsEBAQAA+/fRTtT7nzp1D3759YWFhgdatW2PhwoXIz8/XOJZcLseyZcvg5uYGc3NzBAUF4ejRo411KnplbCTG4572mDfIH3te6o0rK57E3lm9sfAJf/TwsoexWIS7WTL8EHkXi76/jF4f/IX/bDqJFQf/wX//uYfcwhJ9nwIREVGj0WrkSRAE7NixA1999RViY2ORnZ2teWCRCKWlpdXsrRtHjhzB008/jW7dumHixImwsrJCTEwMFAoF1q9fDwC4fPkygoOD0bFjR4SGhiIpKQkffvghBg0ahD/++EPteM899xwOHDiAV155BW3btkVYWBguXryI48ePo2/fvnWKzdBGnh4lX16Ki/FZqpGpf1OkqPqpEYmAADdbhPgpR6V6ejvAUtIgD3ISERE1mAa9bffaa69h06ZNCAwMRL9+/WBvb19tvxUrVtT10LUilUrRrl07hISE4MCBAzUuFzNixAhcvnwZN2/eVF2EL7/8ErNmzcKff/6JJ598EgBw4cIFBAUFYcOGDVi6dCkAoKioCAEBAXBxccG5c+fqHF9zSp4elF1QjIi4zPKn+TIRnaY+kmcsFqGbpx2Cy8sidPO0g8SYNaaIiKhpa9DkycXFBQMHDtRbKYLPP/8cc+bMwfXr19GxY0cUFBTA3NxcLYmSSqVwdHTE4sWLVSNRAFBcXAxHR0dMnDgRX375JQDg9ddfx6ZNm5CVlaV2sdasWYM33ngDiYmJ8PDwqHV8zT15elCatEhVFuFsdCaSc2Rq7WYmYvT0dkBweVmEADcbGLPGFBERNTENWiRTJpNhyJAhWgdXX8eOHYONjQ2Sk5MxZswY3L59G5aWlnjhhRfw0UcfwczMDNeuXUNpaSl69Oihtq+pqSkCAwMRFRWl2hYVFYV27dppXKhevXoBUN7+q0vy1NK42JhhTLc2GNOtDQDgblYhzkZnqEamMvLlOH0nA6fvZAC4BWszYwT5KEsihPg7on0ra5ZFICIig6FV8jR48GBcvHgRoaGhuo6nVu7cuYPS0lKMHj0aM2fOxJo1a3DixAls3rwZOTk52Lt3L1JTUwEArq6uGvu7urri9OnTqtepqak19gOAlJSUh8Yjl8vVKqpLpVKtzqu58HCwwKRenpjUyxOCICA6LV+VTJ2PzYS0qBTHbtzHsRv3AQCOlqaqUakQP0d4OVowmSIioiZLq+Rp69atGDp0KFavXo3Zs2c3ejHM/Px8FBYW4uWXX1Y9XffMM8+guLgY27dvx7vvvguZTHnrSCKRaOxvZmamageUI2k19atof5g1a9Zg1apVWp9PcyYSidC2lTXatrLG9D4+KFMIuJ4ixdnyBY4vxmUhs6AYh66m4tBVZcLbxs68PJlSJlStbVkWgYiImg6tkqf27dtDoVDg7bffxttvvw0zMzMYGalPCBaJRMjNzdVJkA8yNzcHoHxCrqrJkydj+/btCA8Ph4WFsqhjdWvsFRUVqY5Rcbya+lV9v5osX74cS5YsUb2WSqW8zVcDI7EIXdxt0cXdFi8P8ENxqQJXknJUI1NRidlIzpHhwN9JOPB3EgDA19lSlUgF+zrC3tJUz2dBREQtmVbJ07PPPqvX2ypubm74999/0apVK7XtLi4uAIDs7Gz4+fkBgOr2XVWpqalwc3NTvXZ1dUVycnK1/Sre72EkEkm1I1f0aKbGysnkPb0d8MoQQFZchovxWeULHGfgWnIuYtMLEJtegN3nEwEAnVxtVPOlevk4woplEYiIqBFp9a0TFham4zDqpnv37jh69CiSk5PRvn171faKuUnOzs4ICAiAsbExIiMjMWHCBFWf4uJiXL58WW1bYGAgjh8/DqlUqjZpPCIiQtVOjcPc1Aj92zmjfztnAECurAQRsZnlyVQmbt3Pw/VUKa6nSvHlmTgYiUV4zN1WNV/qcS97mJmwLAIRETUcg1yeJSoqCo8//jgmT56MPXv2qLZPnjwZ+/fvR0JCAtzc3DB8+HBcuXIFt27dgrW1NQDgq6++wksvvYQ//vgDw4YNA6BMknr37q1W50kulyMgIACOjo44f/58neJraaUKGlN6nhzhscpRqbPRmUjMKlRrNzUWo4eXfXnBTid0dbeFCcsiEBFRLTT7te1mzpyJr7/+GhMmTMCAAQNw4sQJ7N+/H8uXL8fq1asBKJdvCQkJQadOnVQVxjdu3Ij+/fvjzz//VDvehAkT8PPPP2Px4sXw9/fHN998gwsXLuCvv/5C//796xQbk6fGk5RdqBqVOhudgbQ89blrVhJj9PJxUFU/79jaBmIxn+QjIiJNzT55KikpwerVq7Fz506kpKTAy8sL8+bNwyuvvKLW78yZM1i2bBkuXboEa2trTJgwAWvWrFGNRFUoKirC22+/jd27dyM7Oxtdu3bFe++9h6FDh9Y5NiZP+iEIAmIzCnCufPJ5eGwmch5Yd8/ewgS9fR0R4q+8zefrZMmyCEREBKAFJE9NGZOnpkGhEHA9Vapak+9CXBYKisvU+rSykajmS4X4O6GN3cOfrCQiouaLyZMeMXlqmkrKFLialINz0coJ6H8nZqO4VKHWx8vRQjVfKsTPEU5WfIqSiKilYPKkR0yeDENRSRn+TsjGufKCnVeTclGmUP/j0L6VtapgZ5CvI2zNTfQULRERNTSdJk+JiYlaBeHp6anVfoaOyZNhyisqwYW4LJyNVs6XupGqvsyOWAR0aWOLYD8n9PF3RA8vB5ibsiwCEVFzodPkSSwWazWptqys7NGdmiEmT81DZr4c52OzcC4mA+ExmYjNKFBrNzESoZunsixCH38nPOZuB1NjlkUgIjJUOk2ewsLCtEqepk2bVud9mgMmT81TSo6sfPK5cgJ6am6RWru5iRF6lpdF6OPnhE5uNjBiWQQiIoPBOU96xOSp+RMEAQmZhaoFjsNjMpFVUKzWx8bMWFkWoXxkyt/FimURiIiaMCZPesTkqeVRKATcTssrf5IvAxGxWciTl6r1cbKSlC9wrEymPBws9BQtERFVp1GSp7Nnz+LSpUvIzc2FQqH+yLdIJMLbb7+t7aENGpMnKi1T4J8UqfJJvuhMXIzPgvyBsgju9uaqRCrY1xEuNmZ6ipaIiIAGTp6ysrIwcuRIXLhwAYIgQCQSoeIwFf8vEok4YZzJE5WTl5YhKjEH56IzEB6biajEHJQ+UBbB38VKNTLV29cRdhameoqWiKhlatDkaebMmfj+++/x9ddfIygoCL6+vvjzzz/h4+ODjz76COHh4fjjjz/QqlWrep2EoWLyRI9SIC/Fxfgs1QT0f1JyUfVPokgEdHazQYifE4L9HNHL2wGWEmP9BUxE1AI0aPLk6uqK5557Dps2bUJmZiacnZ1x9OhRDB48GADwzDPPQCKRYO/evdqfgQFj8kR1lVNYjPOxWQgvn4B+Jy1frd1YLEKgh52q+vnjXnaQGLPGFBGRLtX2+1urf8rm5OSgc+fOAAArKysAQH5+5V/2Tz75JN544w1tDk3UItlZmGJYQGsMC2gNAEiTFiE8NhPnojNxNiYDSdkyRCZkIzIhG5/+LxoSYzF6ejsguHzOVICbDYyNWGOKiKgxaJU8ubm54d69ewAAiUQCFxcXXLlyBaNHjwYAJCcn85FsonpwsTHD6MA2GB3YBgBwN6tQtYzMuZhMpOfJcSY6A2eiM7Dhz1uwlhgjyNdBtSZf+1bWELPGFBFRg9Aqeerfvz+OHj2KN998EwAwceJErF+/HkZGRlAoFPj4448xdOhQnQZK1JJ5OFhgooMnJvb0hCAIiE7LVxXrDI/JhLSoFMdupOHYjTQAgKOlKXqXTz4P8XOCt6MF/0FDRKQjWs15unbtGo4ePYp58+ZBIpEgOzsb48ePx//+9z8AyuRq7969cHV11XnAhoBznqgxlSkE/JuSq5p8fiEuC7IS9Sdd3WzNVKNSIf6OcLU111O0RERNl16KZObk5MDIyAjW1ta6OqRBYvJE+lRcqsCVpBxVwc6oxBwUl6nXmPJ1skRw+ahUsJ8jHCxZFoGIiBXG9YjJEzUlsuIyRCZkqeZLXUvKwQMlptDR1UZVY6qXjwOszUz0EywRkR41SvJ06tQpxMbGIjs7Gw8eRiQSYfHixdoe2qAxeaKmLFdWggtxWar5Ujfv5am1G4lF6Opuq5ov1d3LHmYmLItARM1fgyZPly9fxsSJExEdHa2RNKkOzArjTJ7IIKTnyXE+NrN8geMMxGcWqrWbGovRzcMOvX0dEeTrgMc9mUwRUfPUoMlTjx49EBMTg/Xr1yMoKAi2trbV9vPy8qrroZsFJk9kyJKyCxEek4nwGGWNqftSuVq7qZEYj3nYKpMpH0c87mUHC1NWPyciw9egyZO5uTneffddvPbaa/UKsrli8kTNhSAIiM0oQERsFs7HZiIiLlMjmTIuv80X5OuIIB8H9PB2gBWXkiEiA9SgFcbbtm3LmjFELYBIJIKfsxX8nK0wOUhZYyohsxARcZk4H5uFiNhMpOQW4VJiDi4l5mDbiRgYiUUIaGOL3j4OCPJVJlM2nIBORM2IViNPP/30E1599VWcOXMGbdq0aYi4DBpHnqilEAQBSdkynI8tT6biMpGULVPrIxYBnd1sEeTjgCBf5SLHthZMpoio6Wnwp+2+++47hIaGYvDgwXB3d4eRkfoEUpFIhE8++USbQxs8Jk/UkiXnyBARm6m81ReXiYQHJqCLREDH1jYI8nVAkI8jevs6wM6CdaaISP8aNHk6efIkRo0ahby8vBr78Gk7Jk9EAHAvt6jyNl9cJmLTC9TaRSKgs5sN+pQX7Ozp7QBLzpkiIj1o0OSpa9euyM7Oxtdff42goCAmCA9g8kRUszRpESLilIlUeEwmYh5IpozFIgR62CHEX7mcTDdPO0iMWRqBiBpegyZPFhYWWLt2LRYuXFivIJsrJk9EtZcmLUJ4bCbORmfgbHQmknPU50xJjMXo6e2AEH9l0c4ANxsYG4n1FC0RNWcN+rRd586dkZubq3VwREQVXGzMMDqwDUYHKh8+uZtViLPRGarlZDLy5TgTnYEz0RkAbsFaYowgXweE+DkhxN8R7VysIRbz6V8iajxaz3l6/vnn8dNPP6FXr14NEZdB48gTkW4IgoDotHxVMnU+NhPSolK1Po6Wpujt54g+fsrbfF6OFiylQkRaadDbdqNGjcKdO3dw+/ZtdOrUCZ6entU+bXfw4MG6R94MMHkiahhlCgH/puSqRqUuxmVBVqL+YIqbrRmCyxOpPv5OaG1rpqdoicjQNGjy5O3t/ch/2YlEIsTGxtb10M0CkyeixlFcqsDluzk4F6McmYpKzEZJmfpfab5OlgguT6R6+zrCwZJlEYioeg1e54lqxuSJSD8Ki0sRGZ+NszEZOB+TiWvJuVA88DdcR1eb8lEpZVkEa1Y/J6JyTJ70iMkTUdOQKytBRKzyFl94TCZu3VevTWdUvi5fSPmcqce97GFmwrIIRC2VTpOnxMREAICnp6fa60ep6N/SMHkiaprS8+QIj81EePltvgern5sai9Hd0x4hfo4I8XdCV3dbmLAsAlGLodPkSSwWQyQSQSaTwdTUVPX6UVhhnMkTUVOWlF2oGpU6F5OB+1K5WrulqRF6+VSWRejY2oZlEYiaMZ3Wefr6668hEolgYmKi9pqIyJC521tgQg8LTOjhAUEQEJtRoHySLzoD4bGZyCkswfFb6Th+Kx0AYGdhgmBfR9XIlK+TJf8uJGqBOOepAXDkicjwKRQCbtyTIjxGWf38QlwWCorVR9Nb2UgQUr4mXx9/J7SxM9dTtESkCw06YfzFF1/E7NmzERQUVG37hQsX8Pnnn+Prr7+u66GbBSZPRM1PSZkCV5Nyca68YOffidkoLlWo9fFytECInyOC/ZwQ7OsIZ2uJnqIlIm00aPIkFouxe/duTJ48udr2H374AZMnT+acJyZPRM1WUUkZLiVk41xMJs7GZOBqUi7KHqiL0L6VNYL9lLf5gnwdYWvOsghETVmDrm33KCkpKTA35/A1ETVfZiZGCPF3Qoi/E5aiPfKKSnAxPgvnojNxNiYTN1KluHU/D7fu5yHsXDzEIqBLG1tV9fMe3vawMG2Qv4KJqIHVeuTp4MGDquVWwsLC0L9/f/j6+mr0y8nJwbFjx9C9e3ccP35ct9E+xAcffIC33noLnTt3xj///KPWdu7cObz++uu4dOkSbGxsMGHCBKxevRpWVlZq/eRyOd555x18++23yM7ORteuXfH+++/jP//5T51i4cgTEWUVFON8rHK+VHhMJmIzCtTaTYxE6OZhjxB/R4T4OSHQww6mxiyLQKRPOr9tt2bNGqxevRoAUFhYCFNTUxgbq/+rSSQSwdLSEt27d8emTZvQrl27epxC7SUlJaF9+/YQiUTw9vZWS54uX76M4OBgdOzYEaGhoUhKSsKHH36IQYMG4Y8//lA7znPPPYcDBw7glVdeQdu2bREWFoaLFy/i+PHj6Nu3b63jYfJERA9KzZWVTz5XlkVIzS1Sazc3MUIPb3v08VeOTHV2s4URyyIQNSq9znlqbJMmTUJ6ejrKysqQkZGhljyNGDECly9fxs2bN1UX4ssvv8SsWbPw559/4sknnwSgnOQeFBSEDRs2YOnSpQCAoqIiBAQEwMXFBefOnat1PEyeiOhhBEFAQmZh+QLHypGpzIJitT7WZsbo7euIPuVlEdq6WLEsAlEDazHLs5w6dQpPPPEEoqKisGDBArXkSSqVwtHREYsXL8b69etV+xQXF8PR0RETJ07El19+CQB4/fXXsWnTJmRlZaldsDVr1uCNN95AYmIiPDw8ahUTkyciqguFQsCt+3nlxTozERGbiTx5qVofJyuJsr6Un/I2n6ejhZ6iJWq+GmXC+D///IPDhw8jPj4eAODt7Y3hw4ejS5cu9TlsrZWVlWHBggV46aWXqn3Pa9euobS0FD169FDbbmpqisDAQERFRam2RUVFoV27dhoXq1evXgCUt/9qSp7kcjnk8srKxFKpVOtzIqKWRywWoaOrDTq62uDFvj4oLVPgnxSpalTqYnwWMvLl+PVKCn69kgIAcLc3VyVSwX6OaGVjpuezIGo5tEqe5HI5Zs+ejW+//RaCIEAsVk5yVCgUWL58OZ5//nl8+eWXMDU11WmwD/r888+RkJCAY8eOVduempoKAHB1ddVoc3V1xenTp9X61tQPUD5BWJM1a9Zg1apVdYqdiKgmxkZiBHrYIdDDDnMH+kNeWoaoxJzypWQyEJWYg6RsGfZFJmFfZBIAwN/FSjUy1dvXEXYWDfv3L1FLplXytGzZMuzatQtz587FggUL4OfnB5FIhOjoaHz66afYtm0bHBwc8PHHH+s43EqZmZl455138Pbbb8PZ2bnaPjKZDAAgkWgWqjMzM1O1V/StqV/VY1Vn+fLlWLJkieq1VCqt9S0+IqJHkRgbobevMinCf9qhQF6Ki/FZqtt8/6TkIjotH9Fp+dgVngCRCOjsZqMalerl7QBLCcsiEOmKVn+adu/ejRdeeAFbtmxR296+fXt89tlnkEql2L17d4MmT2+99RYcHBywYMGCGvtU1JqqekutQlFRkVotKnNz8xr7VT1WdSQSSbWJFxFRQ7CUGGNgexcMbO8CAMgtLEF4rHJU6lxMJu6k5eOfZCn+SZZix6lYGItFCPSwU1U/7+ZpBzMTIz2fBZHh0ip5KikpQe/evWtsDwkJwW+//aZ1UI9y584d7NixAx9//LHa7bSioiKUlJQgPj4eNjY2qltuFbfvqkpNTYWbm5vqtaurK5KTk6vtB0CtLxFRU2JrYYJhAa0xLKA1ACAtr0g5KhWdiXOxGbibJUNkQjYiE7Lx6f+iITEWo6e3g6r6eZc2tjA2Yo0potrSKnkaOnQo/vzzT8yZM6fa9v/+97+qEgANITk5GQqFAgsXLsTChQs12n18fLBo0SKsWrUKxsbGiIyMxIQJE1TtxcXFuHz5stq2wMBAHD9+HFKpVG3SeEREhKqdiMgQuFibYXRgG4wObAMAuJtVqKwxVT4ylZ4nx5noDJyJzgAAWEuMEeTroKp+3r6VNcSsMUVUI61KFdy6dQsTJkyAn58f5s2bB39/fwDKEaHPPvsMcXFx+OGHHzTmIjk4OOgk6IyMDJw5c0Zj+1tvvYW8vDx88skn8PPzQ5cuXTB8+HBcuXIFt27dgrW1NQDgq6++wksvvYQ//vgDw4YNA6BMknr37q1W50kulyMgIACOjo44f/58reNjqQIiaqoEQUBMer5yTb7y6ufSIvWyCI6WpuhdpSyCt6MFa0xRi9DgRTJVB3jgD1TF4ar7g9bQCwUPHDhQo0jmpUuXEBISgk6dOqkqjG/cuBH9+/fHn3/+qbb/hAkT8PPPP2Px4sXw9/fHN998gwsXLuCvv/5C//79ax0HkyciMhRlCgE3UqU4G60clboQlwVZifrf1W62ZqpRqRB/R7jacu1Sap4aNHlauXKlVv8KWbFiRZ33qYvqkicAOHPmDJYtW4ZLly7B2toaEyZMwJo1a1QjURWKiorw9ttvY/fu3aq17d577z0MHTq0TnEweSIiQ1VcqsDVpBzVMjJRiTkoLlOo9fF1siyfL6V8ms/BkmURqHloMRXGmyImT0TUXMiKy/B3QrZqvtS1pBwoHvjW6Ohqo6ox1cvHAdZmJvoJlqieGiV5KigogFQqhbW1NaysrLQ9TLPD5ImImitpUQkuxGYpk6noTNy6n6fWbiQWoau7rWq+VHcve5ZFIIPRYMlTfHw81q9fj99//x1JSUmq7W3atMHTTz+NpUuXwsfHR/vImwEmT0TUUmTky3E+NhNno5V1puIzC9XaTY3F6O5pr5ov1dXdDiYsi0BNVIMkTwcPHsQLL7yA/Px8eHt7o2vXrrC2tkZeXh6uXr2K+Ph4WFpaYvfu3Rg9erROTsQQMXkiopYqOUdWXmMqA2djMnBfql582MLUCL18HNCnfL5UJ1cblkWgJkPnydP169fx+OOPw9fXF9u3b0e/fv00+pw+fRovv/wyYmNj8ffff6NTp07an4EBY/JERKR8+jouowDnYjJVixxnF5ao9bGzMEFvH+WoVIifE/ycLVkWgfRG58nTlClTcOLECVy9evWh9ZqysrLQtWtXDBo0CN9++23dI28GmDwREWlSKATcvJenSqQi4rKQL1evMeViLVHNlwrxd4S7vYWeoqWWSOfJU5s2bfDSSy9h1apVj+z7zjvv4Kuvvqp2uZOWgMkTEdGjlZYpcDU5t3yB4wxExmdDXqpeFsHTwaJ8TT5lQuVszXVEqeHU9vu71suzZGZmwtvbu1Z9fXx8kJmZWdtDExFRC2RsJMbjnvZ43NMe8wb5o6ikDJcSs5VLyURn4EpSLhKzCpGYVYjvL94FALRrZaWqL9XbxxG2FiyLQI2v1smTk5MT4uLiatU3Li4OTk5OWgdFREQtj5mJkfJ2nZ8TXn2yPfLlpbgYl4Vz5TWmrqdKcft+Pm7fz0fYuXiIRUBAG1vVqFRPb3tYmGq1ZCtRndRpztPx48dx7dq1R8556tKlCwYNGoTdu3frLFBDwtt2RES6l11QjPOxmaoJ6DHpBWrtJkYidPOwL0+mHBHoaQeJMWtMUe012NN2/v7+2LFjB0JCQjT6nDt3DrNnz8adO3fw999/o3PnztqfgQFj8kRE1PDuS4uUo1LRyoQqOUem1m5mIkZPb4fy0SxHBLSxhRHLItBDNEidp59++glTp06FTCaDt7c3HnvsMbU6T3FxcTAzM8M333yDcePG6eREDBGTJyKixiUIAu5myVTLyITHZCAjv1itj7WZMXr7OiLY1xG9fR3RobU1a0yRmgarMB4bG4v169fj0KFDSElJUW13dXXFU089hddeew3+/v7aR94MMHkiItIvQRBwJy0fZ6OVydT52EzkFamXRbA1N0FPbwf09nVAb19HdHS14chUC9coa9tJpVLk5eXB2tqaSUIVTJ6IiJqWMoWAf1NylcvIxGbi7/gsFBSXqfWxNjNGT28HBPkok6nObjYw5lIyLUqjJE9UPSZPRERNW2mZAv+kSBERqxyViozPRt4DBTutJMbo7mWP3r6OCPJ1QJc2tlyXr5lj8qRHTJ6IiAxLmULA9RQpIuKUydSFuCxIH7jNZ2FqVJlM+Tigq7sdTI2ZTDUnTJ70iMkTEZFhK1MIuHlPiojYLGUyFZ+FnAfW5TMzURb5rEimHvOwg5kJSyMYMiZPesTkiYioeVEoBNxOy6tMpuKykFmg/jSfqbEY3T3tlWvz+Tuiq7sdb/MZGCZPesTkiYioeRMEAdFp+Tgfp0ymImKzkJEvV+tjaWqEXj4OquVkOrnasDRCE8fkSY+YPBERtSyCICAmvQDhscoaU+Exmch+4DafnYUJgn0dy0emnODrZAmRiMlUU8LkSY+YPBERtWwKhYAb96QIj1FWP4+IzdQojdDKRqIalerj74Q2duZ6ipYqMHnSIyZPRERUVUmZAleTchFeXgE9MiEbxaUKtT5ejhYI8XNEsJ8Tgn0d4Wwt0VO0LReTJz1i8kRERA9TVFKGSwnZqkWOryTlokyh/nXcvpW1apHjIF9H2Jqb6CnaloPJkx4xeSIiorrIl5fiYlyWajmZ66lStXaxCOjSxhbB5Ysc9/R2gLkpyyLoGpMnPWLyRERE9ZFVUIyI2EzVQsex6QVq7SZGInSrKIvg54RADxbs1AUmT3rE5ImIiHTpXm4RzpUnUueiM5CSW6TWbm5ihJ4+DuXJlCM6u9lykWMtMHnSIyZPRETUUARBQGJWIc5GK+dLhcdkahTstDEzRu8qZRHaulixLEItMHnSIyZPRETUWARBwO37+ar5UhGxmRqLHDtZSZQlEcpv83k4mDOZqgaTJz1i8kRERPpSWqbAvylSnC0flboYn4WiEvWyCG3szBFSXl8q0MMO7vbmMOZSMkye9InJExERNRXy0jJEJebgXIyy+nlUYg5KHyiLYGIkgpejJXydLOHrbAVfZ0v4OVvBz9kSdhameoq88TF50iMmT0RE1FQVyEtxMT4L4TGZCI/NxK17eZA/ULCzKgdL0/KkSplY+ZUnV54OFs1u4WMmT3rE5ImIiAyFQiEgJVeG2PQCxKbnIzajADHp+YhNL0DqA0/1VWUsFsHTwUKVVPk6WcLPRflfB0tTg5xTxeRJj5g8ERFRc1BYXKpMqjLKE6t0ZWIVl1GAwgfW6qvK1twEPk6WcLc3Rxs7c7jZqf/Xxty4SSZXTJ70iMkTERE1Z4Ig4J60SDVaFVOeYMWk5SMlV4ZHZRaWpkZwK0+mlAmVWZX/N0drWzO93BJk8qRHTJ6IiKilKiopQ1xGAeIzCpCcI0NKThFScmRIyZUhJUeGjPziRx5DJAJaWZvBrTypalMl0XKzM0MbO3PYmpvofPSKyZMeMXkiIiKqXlFJmTKZKk+qlAlWRXJVhOQcGYofMoG9wt9vDYGjlUSnsdX2+9tYp+9KRERE9BBmJkbl5RCsqm1XKARkFhSXJ1gyjdGr5GwZCovL4GCpvxIKTJ6IiIioyRCLRXC2lsDZWoLHPOyq7SMvLdPrhPPmVaCBiIiImj2JsZFe35/JExEREVEdGGTydPHiRcyfPx+dO3eGpaUlPD09MWHCBNy+fVuj740bNzBs2DBYWVnBwcEBL7zwAtLT0zX6KRQKrF+/Hj4+PjAzM0PXrl2xd+/exjgdIiIiMiAGOedp3bp1OHv2LMaPH4+uXbvi3r172LJlCx5//HGcP38eAQEBAICkpCT0798ftra2WL16NfLz8/Hhhx/i2rVruHDhAkxNKyebvfnmm1i7di1mzZqFnj174uDBg5g8eTJEIhEmTZqkr1MlIiKiJsYgSxWcO3cOPXr0UEt+7ty5gy5dumDcuHHYvXs3AGDu3LkICwvDzZs34enpCQA4duwY/vOf/2D79u0IDQ0FACQnJ8PHxwehoaHYsmULAGUBsAEDBiAuLg7x8fEwMqr9/VWWKiAiIjI8tf3+NsjbdiEhIWqJEwC0bdsWnTt3xo0bN1TbfvzxRzz11FOqxAkAhgwZgnbt2mHfvn2qbQcPHkRJSQnmzp2r2iYSiTBnzhwkJSUhPDy8Ac+GiIiIDIlBJk/VEQQB9+/fh5OTEwDlaFJaWhp69Oih0bdXr16IiopSvY6KioKlpSU6duyo0a+i/WHkcjmkUqnaDxERETVPzSZ52rNnD5KTkzFx4kQAQGpqKgDA1dVVo6+rqyuysrIgl8tVfVu1aqVRM6Ji35SUlIe+95o1a2Bra6v68fDwqPf5EBERUdPULJKnmzdvYt68eQgODsa0adMAADKZDAAgkWiWbjczM1PrI5PJatWvJsuXL0dubq7q5+7du9qfDBERETVpBvm0XVX37t3DyJEjYWtriwMHDqgmdpubmwOAanSpqqKiIrU+5ubmtepXE4lEUm3yRURERM2PQY885ebmYvjw4cjJycF///tfuLm5qdoqbrlV3L6rKjU1FQ4ODqqEx9XVFffu3cODDx5W7Fv1uERERNSyGWzyVFRUhKeffhq3b9/GoUOH0KlTJ7X2Nm3awNnZGZGRkRr7XrhwAYGBgarXgYGBKCwsVHtSDwAiIiJU7URERESAgSZPZWVlmDhxIsLDw7F//34EBwdX2+/ZZ5/FoUOH1OYg/fXXX7h9+zbGjx+v2jZ69GiYmJhg69atqm2CIODzzz9HmzZtEBIS0nAnQ0RERAbFIOc8vfrqq/j111/x9NNPIysrS1UUs8KUKVMAAG+88Qb279+PQYMGYdGiRcjPz8eGDRvQpUsXzJgxQ9Xf3d0dr7zyCjZs2ICSkhL07NkTv/zyC06fPo09e/bUqUAmERERNW8GWWF84MCBOHnyZI3tVU/p33//xZIlS3DmzBmYmppi5MiR2LhxI1q1aqW2j0KhwLp167B9+3akpqaibdu2WL58OZ5//vk6x5ebmws7OzvcvXuXFcaJiIgMhFQqhYeHB3JycmBra1tjP4NMnpq6pKQk1noiIiIyUHfv3oW7u3uN7UyeGoBCoUBKSgqsra01Cm/WR0VGzBGthsXr3Dh4nRsPr3Xj4HVuHA15nQVBQF5eHtzc3CAW1zwt3CDnPDV1YrH4oRlrfdnY2PAPZiPgdW4cvM6Nh9e6cfA6N46Gus4Pu11XwSCftiMiIiLSFyZPRERERHXA5MmASCQSrFixgkvBNDBe58bB69x4eK0bB69z42gK15kTxomIiIjqgCNPRERERHXA5ImIiIioDpg8EREREdUBkyciIiKiOmDy1ATI5XIsW7YMbm5uMDc3R1BQEI4ePVqrfZOTkzFhwgTY2dnBxsYGo0ePRmxsbANHbJi0vc63bt3C4sWLERISAjMzM4hEIsTHxzd8wAZK2+v8008/YeLEifD19YWFhQXat2+PV199FTk5OQ0ftIHS9lr//PPPGDp0KNzc3CCRSODu7o5x48bhn3/+aYSoDU99/o6u6j//+Q9EIhHmz5/fAFEaPm2v88qVKyESiTR+zMzMGixWVhhvAqZPn44DBw7glVdeQdu2bREWFoYRI0bg+PHj6Nu3b4375efnY9CgQcjNzcUbb7wBExMTfPTRRxgwYAAuX74MR0fHRjyLpk/b6xweHo5PP/0UnTp1QseOHXH58uXGC9oAaXudQ0ND4ebmhilTpsDT0xPXrl3Dli1bcPjwYVy6dAnm5uaNeBaGQdtrfe3aNdjb22PRokVwcnLCvXv38PXXX6NXr14IDw/HY4891ohn0fRpe52r+umnnxAeHt7AkRq2+l7nbdu2wcrKSvXayMio4YIVSK8iIiIEAMKGDRtU22QymeDn5ycEBwc/dN9169YJAIQLFy6ott24cUMwMjISli9f3mAxG6L6XOfMzExBKpUKgiAIGzZsEAAIcXFxDRmuwarPdT5+/LjGtm+++UYAIHzxxRe6DtXg1edaV+fevXuCsbGxMHv2bF2GafB0cZ1lMpng7e0tvPvuuwIAYd68eQ0VrsGqz3VesWKFAEBIT09v6DBVeNtOzw4cOAAjIyOEhoaqtpmZmWHmzJkIDw/H3bt3H7pvz5490bNnT9W2Dh06YPDgwdi3b1+Dxm1o6nOdHRwcYG1t3RhhGrz6XOeBAwdqbBs7diwA4MaNGzqP1dDV51pXx8XFBRYWFrxN+gBdXOf169dDoVBg6dKlDRmqQdPFdRYEAVKpFEIjlK9k8qRnUVFRaNeuncbihr169QKAGm8RKRQKXL16FT169NBo69WrF2JiYpCXl6fzeA2VtteZ6kbX1/nevXsAACcnJ53E15zo4lrn5OQgPT0d165dw0svvQSpVIrBgwc3RLgGq77XOTExEWvXrsW6det46/khdPF59vX1ha2tLaytrTFlyhTcv3+/IUIFwDlPepeamgpXV1eN7RXbUlJSqt0vKysLcrn8kfu2b99eh9EaLm2vM9WNrq/zunXrYGRkhHHjxukkvuZEF9e6d+/euHXrFgDAysoKb731FmbOnKnbQA1cfa/zq6++im7dumHSpEkNEl9zUZ/rbG9vj/nz5yM4OBgSiQSnT5/GZ599hgsXLiAyMlIjIdMFJk96JpPJql2fp+IpAZlMVuN+ALTatyXS9jpT3ejyOn/33Xf46quv8Prrr6Nt27Y6i7G50MW13rlzJ6RSKWJjY7Fz507IZDKUlZVBLOZNiQr1uc7Hjx/Hjz/+iIiIiAaLr7moz3VetGiR2utnn30WvXr1wvPPP4+tW7fi//7v/3QbLJg86Z25uTnkcrnG9qKiIlV7TfsB0Grflkjb60x1o6vrfPr0acycORNDhw7FBx98oNMYmwtdXOvg4GDV/0+aNAkdO3YEAHz44Yc6itLwaXudS0tLsXDhQrzwwgtq81Kperr+O3ry5Ml49dVXcezYsQZJnvjPCz1zdXVFamqqxvaKbW5ubtXu5+DgAIlEotW+LZG215nqRhfX+cqVKxg1ahQCAgJw4MABGBvz33jV0fVn2t7eHk888QT27Nmjk/iaC22v865du3Dr1i3Mnj0b8fHxqh8AyMvLQ3x8PAoLCxssbkPTEH9He3h4ICsrq96xVYfJk54FBgbi9u3bkEqlatsrhnkDAwOr3U8sFqNLly6IjIzUaIuIiICvry+fEKtC2+tMdVPf6xwTE4Nhw4bBxcUFhw8fVqvZQuoa4jMtk8mQm5uri/CaDW2vc2JiIkpKStCnTx/4+PiofgBlYuXj44MjR440aOyGRNefZ0EQEB8fD2dnZ12FqIbJk56NGzcOZWVl2LFjh2qbXC7Hzp07ERQUBA8PDwDKP4g3b97U2PfixYtqCdStW7fwv//9D+PHj2+cEzAQ9bnOVHv1uc737t3Dk08+CbFYjD///LPB/tJrLupzrdPS0jSOFx8fj7/++qvaJ3hbMm2v86RJk/Dzzz9r/ADAiBEj8PPPPyMoKKhxT6YJq8/nOT09XeN427ZtQ3p6OoYNG9YwATdaRSmq0fjx4wVjY2PhtddeE7Zv3y6EhIQIxsbGwsmTJ1V9BgwYIDz465JKpYKfn5/g4uIirF+/Xvjoo48EDw8Pwc3NTUhLS2vs02jytL3OOTk5wnvvvSe89957wrBhwwQAwquvviq89957wubNmxv7NJo8ba/zY489JgAQXn/9deHbb79V+zly5Ehjn4ZB0PZau7i4CM8995ywbt06YceOHcJrr70mODg4CGZmZsLZs2cb+zSaPG2vc3XAIpk10vY6m5ubC9OnTxc2btwofPbZZ8Jzzz0niEQiITAwUCgoKGiQWJk8NQEymUxYunSp0Lp1a0EikQg9e/YU/vvf/6r1qekP5t27d4Vx48YJNjY2gpWVlfDUU08Jd+7caazQDYq21zkuLk4AUO2Pl5dXI56BYdD2Otd0jQEIAwYMaMQzMBzaXusVK1YIPXr0EOzt7QVjY2PBzc1NmDRpknD16tXGDN9g1Ofv6AcxeaqZttf5pZdeEjp16iRYW1sLJiYmgr+/v7Bs2TLVyhANQSQIjVCKk4iIiKiZ4JwnIiIiojpg8kRERERUB0yeiIiIiOqAyRMRERFRHTB5IiIiIqoDJk9EREREdcDkiYiIiKgOmDwRERER1QGTJyIiIqI6YPJEREREVAdMnoiIiIjqgMkTUTMSFhYGkUiE+Ph4fYdSZxcvXkRISAgsLS0hEolw+fLlOh9j5cqVEIlEyMjI0H2ApNIUP2f83VNjYvJEVEsVXxgikQhnzpzRaBcEAR4eHhCJRHjqqaf0EGHDunLlCsaPH482bdpAIpGgVatWGDVqFFJTU+t97JKSEowfPx5ZWVn46KOP8O2338LLy6vG/ufOncPKlSuRk5NT7/duafR97fT9/kS6wOSJqI7MzMzw3XffaWw/efIkkpKSIJFI9BCV0gsvvACZTPbQxEMbqamp6Nu3L+Lj4/Haa69hx44dWL58OQRBgCAI9T5+TEwMEhISsHTpUoSGhmLKlCmwt7evsf+5c+ewatUqfgFrQRfXrj6fM/7uqDkw1ncARIZmxIgR2L9/Pz799FMYG1f+Efruu+/QvXt3nd42KCgogKWlZa37GxkZwcjISGfvX+HQoUPIz8/Hxx9/jD59+qi2v/LKKzo5flpaGgDAzs5OJ8ej6hUUFOjkOA31OSMyFBx5Iqqj5557DpmZmTh69KhqW3FxMQ4cOIDJkydr9E9ISMDcuXPRvn17mJubw9HREePHj9eYL1IxZ+P69euYPHky7O3t0bdvX1X7iRMn0KNHD5iZmcHPzw/bt29X7VOhurkoFX2io6Mxffp02NnZwdbWFjNmzEBhYWGtzjkoKAgSiQTDhw/H1KlTsXfvXuTl5dVq36ioKAwfPhw2NjawsrLC4MGDcf78eVX79OnTMWDAAADA+PHjIRKJMHDgwBqPt3LlSrz22msAAB8fH9Wt1KrnnJOTU6tzTU5OxosvvohWrVpBIpGgc+fO+Prrrx95TtOnT4e3t3e1sVX9fVTdVpvrn5ycjJkzZ8LNzQ0SiQQ+Pj6YM2cOiouL6xxzTZ+nh1272n5Wtf2cPex3d/z4cYhEIvz8888a5/Ldd99BJBIhPDy8+l9IFRkZGZgwYQJsbGzg6OiIRYsWoaioSKPfoz6XMpkMHTp0QIcOHSCTyVTbs7Ky4OrqipCQEJSVlT0yHmqeOPJEVEfe3t4IDg7G3r17MXz4cADAH3/8gdzcXEyaNAmffvqpWv+LFy/i3LlzmDRpEtzd3REfH49t27Zh4MCBuH79OiwsLNT6jx8/Hm3btsXq1atVt8SioqIwbNgwuLq6YtWqVSgrK8O7774LZ2fnWsc9YcIE+Pj4YM2aNbh06RK+/PJLuLi4YN26dY/cV6FQoHfv3nj55ZeRlpaGNWvWYMmSJfj555/Ru3fvGvf7999/0a9fP9jY2OD111+HiYkJtm/fjoEDB+LkyZMICgrC7Nmz0aZNG6xevRoLFy5Ez5490apVqxqP+cwzz+D27dvYu3cvPvroIzg5OQGA2rWozbnev38fvXv3hkgkwvz58+Hs7Iw//vgDM2fOhFQq1dmoWm1jSklJQa9evZCTk4PQ0FB06NABycnJOHDgAAoLC2FqaqpVzFU/TyUlJTh//nyN166un9W6nufDfndeXl7w8PDAnj17MHbsWLVj7tmzB35+fggODq7V+3t7e2PNmjU4f/48Pv30U2RnZ2PXrl2qPrX5XJqbm+Obb75Bnz598Oabb2LTpk0AgHnz5iE3NxdhYWEcfWvJBCKqlZ07dwoAhIsXLwpbtmwRrK2thcLCQkEQBGH8+PHCoEGDBEEQBC8vL2HkyJGq/Sr6VBUeHi4AEHbt2qXatmLFCgGA8Nxzz2n0f/rppwULCwshOTlZte3OnTuCsbGxUPWPcUWMcXFxGsd98cUX1Y45duxYwdHR8ZHn/e+//wpOTk7C1atXVdukUqng6ekptG/f/qH7jhkzRjA1NRViYmJU21JSUgRra2uhf//+qm3Hjx8XAAj79+9/ZDyCIAgbNmzQOE9BqNu5zpw5U3B1dRUyMjLUtk+aNEmwtbWt9vdWYdq0aYKXl5fG9or31yamqVOnCmKxWLh48aLGcRUKRZ1jrunzVNO1E4Taf1br8zl72PsvX75ckEgkQk5OjmpbWlqaYGxsLKxYsUKjf1UV7z9q1Ci17XPnzhUACFeuXFFtq+3nsiImsVgsnDp1Sti/f78AQPj4448fGgs1f7xtR6SFCRMmQCaT4dChQ8jLy8OhQ4eqvWUHAObm5qr/LykpQWZmJvz9/WFnZ4dLly5p9H/55ZfVXpeVleHYsWMYM2YM3NzcVNv9/f1VI1+18eBx+/Xrh8zMTEil0ofuN2PGDIwaNQpdunRRbbO2tsZTTz2FW7du1bh/WVkZjhw5gjFjxsDX11e13dXVFZMnT8aZM2ce+d7aetS5CoKAH3/8EU8//TQEQUBGRobqZ+jQocjNza32d9NQMSkUCvzyyy94+umn0aNHD419RSKR1jE/+L4PU9fPal3P81GmTp0KuVyOAwcOqLb98MMPKC0txZQpU2r1/vPmzVN7vWDBAgDA4cOHAdT9c7ly5Up07twZ06ZNw9y5czFgwAAsXLiwVrFQ88XkiUgLzs7OGDJkCL777jv89NNPKCsrw7hx46rtK5PJ8M4778DDwwMSiQROTk5wdnZGTk4OcnNzNfr7+PiovU5LS4NMJoO/v79G3+q21cTT01PtdcXTbNnZ2TXuc+HCBVy4cAGjRo3SaCstLQUAmJiYVLtveno6CgsL0b59e422jh07QqFQ4O7du7WOvy4eda7p6enIycnBjh074OzsrPYzY8YMAJWT2BsjpvT0dEilUgQEBNS4v7YxP/h5epi6flaro83nrEKHDh3Qs2dP7NmzR7Vtz5496N27d60/623btlV77efnB7FYrJqfVdfPpampKb7++mvExcUhLy8PO3fu1JjXRi0P5zwRaWny5MmYNWsW7t27h+HDh9f4pNiCBQuwc+dOvPLKKwgODoatrS1EIhEmTZoEhUKh0b/qv/51qab5GcJDSg1EREQAUH6pPejy5cuqicVNzaPOteK6T5kyBdOmTau2b9euXWs8fk1fng+bQKzN9a9K25jr8vup62e1OvU9z6lTp2LRokVISkqCXC7H+fPnsWXLllqfw4N0kej8+eefAICioiLcuXOnTgkpNU9Mnoi0NHbsWMyePRvnz5/HDz/8UGO/AwcOYNq0adi4caNqW1FRUa3r3Li4uMDMzAzR0dEabdVt06XMzEwAyn99VxUTE4OLFy/ijTfeqHFfZ2dnWFhY4NatWxptN2/ehFgshoeHh1Zx1fcL0dnZGdbW1igrK8OQIUPqvL+9vX21v7+EhASt47GxscE///zz0D71ibnCw65dfT+r9X1/AJg0aRKWLFmCvXv3QiaTwcTEBBMnTqz18R9MbqKjo6FQKFRPR9b1c3n16lW8++67mDFjBi5fvoyXXnoJ165dg62tba1jouaHt+2ItGRlZYVt27Zh5cqVePrpp2vsZ2RkpPGv7s2bN9f6MWcjIyMMGTIEv/zyC1JSUlTbo6Oj8ccff2gXfC1VzLE6duyYaptcLsfs2bNhZ2eH2bNn17ivkZERnnzySRw8eFDtkfb79+/ju+++Q9++fWFjY6NVXBW1r7T9UjcyMsKzzz6LH3/8sdqEJT09/aH7+/n5ITc3F1evXlVtS01NrfYx+9oQi8UYM2YMfvvtN0RGRmq0C4JQ75grPOza1fezWt/3BwAnJycMHz4cu3fvxp49ezBs2DDVU3m18dlnn6m93rx5MwCo5gfW5XNZUlKC6dOnw83NDZ988gnCwsJw//59LF68uNbxUPPEkSeieqjp9klVTz31FL799lvY2tqiU6dOCA8Px7Fjx+Do6Fjr91m5ciWOHDmCPn36YM6cOSgrK8OWLVsQEBCg1RpwtTV27Fi8/vrrWLx4Me7evQs7Ozvs3r0b165dw/79+x85cvT+++/j6NGj6Nu3L+bOnQtjY2Ns374dcrkc69ev1zqu7t27AwDefPNNTJo0CSYmJg9NYKuzdu1aHD9+HEFBQZg1axY6deqErKwsXLp0CceOHUNWVlaN+06aNAnLli3D2LFjsXDhQhQWFmLbtm1o166d1hPNV69ejSNHjmDAgAEIDQ1Fx44dkZqaiv379+PMmTOws7OrV8wVarp2lpaWOvms1uf9K0ydOlU1h/C9996r0/Hj4uIwatQoDBs2DOHh4di9ezcmT56Mxx57TNWntp/L999/H5cvX8Zff/0Fa2trdO3aFe+88w7eeustjBs3DiNGjKjPpSBDpqen/IgMTtVSBQ/zYKmC7OxsYcaMGYKTk5NgZWUlDB06VLh586bg5eUlTJs2TdWv4lHr9PT0ao/7119/Cd26dRNMTU0FPz8/4csvvxReffVVwczMTCPG6h4hf/C41fWtzvnz54U+ffoIZmZmgo2NjTB8+HDh3LlzD92nqkuXLglDhw4VrKysBAsLC2HQoEEa+9e1VIEgCMJ7770ntGnTRhCLxarzqOu53r9/X5g3b57g4eEhmJiYCK1btxYGDx4s7Nix45Hvf+TIESEgIEAwNTUV2rdvL+zevfuhpQpqE1NCQoIwdepUwdnZWZBIJIKvr68wb948QS6X1znmh32eqrt2glD7z2p9P2c1vX8FuVwu2NvbC7a2toJMJtOIvzoV73/9+nVh3LhxgrW1tWBvby/Mnz+/2mM86nP5999/C8bGxsKCBQvU9istLRV69uwpuLm5CdnZ2bWKjZofkSDoYGEqItKLMWPG4N9//8WdO3f0HQqRzpSWlsLNzQ1PP/00vvrqK32HQ6SBc56IDETVJSIA5cTYw4cPP3QpEyJD9MsvvyA9PR1Tp07VdyhE1eLIE5GBcHV1xfTp0+Hr64uEhARs27YNcrkcUVFRGrVtiAxRREQErl69ivfeew9OTk46L1RKpCucME5kIIYNG4a9e/fi3r17kEgkCA4OxurVq5k4UbOxbds27N69G4GBgQgLC9N3OEQ14sgTERERUR1wzhMRERFRHTB5IiIiIqoDJk9EREREdcDkiYiIiKgOmDwRERER1QGTJyIiIqI6YPJEREREVAdMnoiIiIjqgMkTERERUR0weSIiIiKqg/8H/3OYlxqYL9UAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "df[[\"profit\"]].plot()\n",
        "plt.ylim([16001, 17999])\n",
        "plt.xlabel(\"Margin $\\delta$ of the uncertainty box\")\n",
        "plt.ylabel(\"Profit\")\n",
        "plt.show()\n",
        "df[[\"logic\", \"memory\"]].plot()\n",
        "plt.xlabel(\"Margin $\\delta$ of the uncertainty box\")\n",
        "plt.ylabel(\"Optimal number of produced chips\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WNDlWBWFK3iJ"
      },
      "source": [
        "## Cardinality-constrained uncertainty set\n",
        "\n",
        "Let us now make different assumptions regarding the uncertainty related to the copper consumption. More specifically, we now assume that each uncertain coefficient $z_j$ may deviate by at most $\\pm \\delta$ from the nominal value $\\bar{z}_j$ but no more than $\\Gamma$ will actually deviate.\n",
        "\n",
        "$$\n",
        "\\begin{array}{rrcrcl}\n",
        "\\max    &  12 x_1 & + &   9 x_2               \\\\\n",
        "\\text{s.t.}    &     x_1 &   &         & \\leq & 1000 \\\\\n",
        "        &         &   &     x_2 & \\leq & 1500 \\\\\n",
        "        &     x_1 & + &     x_2 & \\leq & 1750 \\\\\n",
        "        & z_1 x_1 & + & z_2 x_2 & \\leq & 4800 & \\forall \\, y \\in \\mathbb{R}^2 \\,:\\, z_j=\\bar{z}_j+\\delta y_j, \\, \\|y\\|_\\infty \\leq 1, \\, \\|y\\|_1\\leq \\Gamma \\\\\n",
        "        &     x_1 & , &     x_2 & \\geq & 0    \\\\\n",
        "\\end{array}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Robust counterpart of cardinality-constrained uncertainty\n",
        "Lagrange duality yields the following modification to the problem as equivalent to the robust model stated above:\n",
        "\n",
        "$$\n",
        "\\begin{array}{rrcrcrcrcrcrcl}\n",
        "\\max    &  12 x_1 & + &   9 x_2               \\\\\n",
        "\\text{s.t.}    &     x_1 &   &         & & & & & & & \\leq & 1000 \\\\\n",
        "        &         &   &     x_2 & & & & & & & \\leq & 1500 \\\\\n",
        "        &     x_1 & + &     x_2 & & & & & & & \\leq & 1750 \\\\\n",
        "        & \\bar{z}_1 x_1 & + & \\bar{z}_2 x_2 & + & \\lambda\\Gamma & + & t_1 & + & t_2 & \\leq & 4800 \\\\\n",
        "        &-\\delta x_1 &   &         & + & \\lambda & + & t_1 &   &     & \\geq & 0 \\\\\n",
        "        &         &   &-\\delta x_2 & + & \\lambda &   &     & + & t_2 & \\geq & 0 \\\\\n",
        "        &\\delta x_1 &   &         & + & \\lambda & + & t_1 &   &     & \\geq & 0 \\\\\n",
        "        &         &   &\\delta x_2 & + & \\lambda &   &     & + & t_2 & \\geq & 0 \\\\\n",
        "        &     x_1 & , &     x_2 & , & \\lambda & , & t_1 & , & t_2 & \\geq & 0    \\\\\n",
        "\\end{array}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Overwriting BIM_robust_cardinality.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile BIM_robust_cardinality.mod\n",
        "\n",
        "set CHIPS;\n",
        "\n",
        "param profits{CHIPS};\n",
        "param copper{CHIPS};\n",
        "\n",
        "var x{CHIPS} >= 0, integer;\n",
        "\n",
        "maximize Profit: sum {c in CHIPS} profits[c] * x[c];\n",
        "\n",
        "s.t. Silicon: x['logic'] <= 1000;\n",
        "s.t. Germanium: x['memory'] <= 1500;\n",
        "s.t. Plastic: sum {c in CHIPS} x[c] <= 1750;\n",
        "\n",
        "param Gamma;\n",
        "param delta;\n",
        "    \n",
        "var t{CHIPS} >= 0;\n",
        "var lam >= 0;\n",
        "\n",
        "s.t. RobustCopper:\n",
        "    sum {c in CHIPS} copper[c] * x[c]\n",
        "        + Gamma * lam\n",
        "        + sum {c in CHIPS} t[c]\n",
        "        <= 4800;\n",
        "\n",
        "s.t. UpRule{c in CHIPS}:\n",
        "    t[c] >= delta * x[c] - lam;\n",
        "s.t. DownRule{c in CHIPS}:\n",
        "    t[c] >= -delta * x[c] - lam;\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "pi13XIN0K3iJ"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17673\n",
            "4 simplex iterations\n",
            "1 branching nodes\n",
            "x = ({'logic': 641.0, 'memory': 1109.0})\n",
            "optimal value = 17673.00\n"
          ]
        }
      ],
      "source": [
        "def BIMWithBudgetUncertainty(delta, gamma):\n",
        "    ampl = AMPL()\n",
        "    ampl.read(\"BIM_robust_cardinality.mod\")\n",
        "\n",
        "    ampl.set[\"CHIPS\"] = chips\n",
        "    ampl.param[\"profits\"] = profits\n",
        "    ampl.param[\"copper\"] = copper\n",
        "\n",
        "    ampl.param[\"delta\"] = delta\n",
        "    ampl.param[\"Gamma\"] = gamma\n",
        "\n",
        "    ampl.option[\"solver\"] = SOLVER_MILP\n",
        "    ampl.solve()\n",
        "\n",
        "    return ampl\n",
        "\n",
        "\n",
        "ampl = BIMWithBudgetUncertainty(0.01, 2)\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Adversarial approach for the budgeted uncertainty set\n",
        "\n",
        "Instead of adopting the approach of robust counterparts, we could also use the adversarial approach where we initially solve the problem for the nominal value of the data. Then, we iteratively search for scenarios that make the current solution violate the copper constraint, and pre-solve the problem to take this scenario into account. To do so, we need to slightly modify our problem formulation function to allow for many scenarios for the parameter $z$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Overwriting BIM_robust_cardinality_adversarial.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile BIM_robust_cardinality_adversarial.mod\n",
        "\n",
        "set CHIPS;\n",
        "\n",
        "param profits{CHIPS};\n",
        "param copper{CHIPS};\n",
        "\n",
        "var x{CHIPS} >= 0;\n",
        "\n",
        "maximize Profit: sum {c in CHIPS} profits[c] * x[c];\n",
        "\n",
        "s.t. Silicon: x['logic'] <= 1000;\n",
        "s.t. Germanium: x['memory'] <= 1500;\n",
        "s.t. Plastic: sum {c in CHIPS} x[c] <= 1750;\n",
        "\n",
        "set CUTS;\n",
        "    \n",
        "param Z{CUTS, CHIPS};\n",
        "\n",
        "s.t. Balance{i in CUTS}:\n",
        "    sum {c in CHIPS}\n",
        "        copper[c] * x[c] * (1 + Z[i, c]) <= 4800;\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [],
      "source": [
        "def BIMWithSetOfScenarios(Z=[{\"logic\": 0, \"memory\": 0}]):\n",
        "    ampl = AMPL()\n",
        "    ampl.read(\"BIM_robust_cardinality_adversarial.mod\")\n",
        "\n",
        "    ampl.set[\"CHIPS\"] = chips\n",
        "    ampl.param[\"profits\"] = profits\n",
        "    ampl.param[\"copper\"] = copper\n",
        "\n",
        "    dfZ = pd.DataFrame(Z)\n",
        "    ampl.set[\"CUTS\"] = list(dfZ.index)\n",
        "    ampl.param[\"Z\"] = dfZ.T.unstack(1)\n",
        "\n",
        "    ampl.option[\"solver\"] = SOLVER_MILP\n",
        "    ampl.solve()\n",
        "\n",
        "    return ampl"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We also need a function that for a given solution finds the worst-possible realization of the uncertainty restricted by the parameters $\\Gamma$ and $\\delta$. In other words, its role is to solve the following maximization problem for a given solution $(\\bar{x}_1, \\bar{x}_2)$:\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "\\max \\ & (\\bar{z}_1 + \\delta y_1) \\bar{x}_1 + (\\bar{z}_2 + \\delta y_2) \\bar{x}_2 - 4800 \\\\\n",
        "\\text{s.t.} \\ & |y_1| + |y_2| \\leq \\Gamma \\\\\n",
        "& -1 \\leq y_i \\leq 1 && i = 1, 2.\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "Such a function is implemented below and takes as argument also the maximum magnitude of the individual deviations $\\delta$ and the total budget $\\Gamma$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Overwriting BIM_robust_cardinality_pessimizer.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile BIM_robust_cardinality_pessimizer.mod\n",
        "\n",
        "set CHIPS;\n",
        "param copper{CHIPS};\n",
        "\n",
        "var z{CHIPS};\n",
        "var u{CHIPS} >= 0;\n",
        "\n",
        "s.t. AbsValue1{i in CHIPS}:\n",
        "    z[i] <= u[i];\n",
        "\n",
        "s.t. AbsValue2{i in CHIPS}:\n",
        "    -z[i] <= u[i];\n",
        "\n",
        "s.t. AbsValueLE1{i in CHIPS}:\n",
        "    u[i] <= 1.0;\n",
        "\n",
        "param x{CHIPS};\n",
        "param Gamma;\n",
        "param delta;\n",
        "\n",
        "s.t. Budget:\n",
        "    sum {i in CHIPS} u[i] <= Gamma;\n",
        "\n",
        "maximize Violation:\n",
        "        -4800\n",
        "        + sum {c in CHIPS}\n",
        "            copper[c] * x[c] * (1 + delta * z[c]);\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [],
      "source": [
        "def BIMPessimization(x, delta, gamma):\n",
        "    ampl = AMPL()\n",
        "    ampl.read(\"BIM_robust_cardinality_pessimizer.mod\")\n",
        "\n",
        "    ampl.set[\"CHIPS\"] = chips\n",
        "    ampl.param[\"copper\"] = copper\n",
        "\n",
        "    ampl.param[\"x\"] = x\n",
        "    ampl.param[\"Gamma\"] = gamma\n",
        "    ampl.param[\"delta\"] = delta\n",
        "\n",
        "    ampl.option[\"solver\"] = SOLVER_MILP\n",
        "    ampl.solve()\n",
        "\n",
        "    worst_z = ampl.get_variable(\"z\").to_dict()\n",
        "\n",
        "    return worst_z, ampl.get_value(\"Violation\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We wrap the two functions above into a loop of the adversarial approach, which begins with a non-perturbation assumption and gradually generates violating scenarios, reoptimizing until the maximum constraint violation is below a tolerable threshold."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 17700\n",
            "2 simplex iterations\n",
            "0 barrier iterations\n",
            "\n",
            "Iteration #0\n",
            "Current solution: \n",
            "x['logic']= 650.00\n",
            "x['memory']= 1100.00\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 740\n",
            "1 simplex iterations\n",
            "0 barrier iterations\n",
            "Violation found: z['logic'] = 1.0,  z['memory'] = 0.5, constraint violation: 740.00\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective 13950\n",
            "1 simplex iterations\n",
            "0 barrier iterations\n",
            "\n",
            "Iteration #1\n",
            "Current solution: \n",
            "x['logic']= 37.50\n",
            "x['memory']= 1500.00\n",
            "HiGHS 1.5.1: HiGHS 1.5.1: optimal solution; objective -1035\n",
            "1 simplex iterations\n",
            "0 barrier iterations\n",
            "No violation found. Stopping the procedure.\n"
          ]
        }
      ],
      "source": [
        "# Parameters\n",
        "adversarial_converged = False\n",
        "stopping_precision = 0.1\n",
        "max_iterations = 5\n",
        "adversarial_iterations = 0\n",
        "delta = 0.2\n",
        "gamma = 1.5\n",
        "chips = [\"logic\", \"memory\"]\n",
        "\n",
        "# Initialize the null scenario - no perturbation\n",
        "Z = [{\"logic\": 0, \"memory\": 0}]\n",
        "\n",
        "while (not adversarial_converged) and (adversarial_iterations < max_iterations):\n",
        "    # Building and solving the master problem\n",
        "    ampl = BIMWithSetOfScenarios(Z)\n",
        "\n",
        "    # Saving the current solution\n",
        "    x = ampl.get_variable(\"x\").to_dict()\n",
        "\n",
        "    print(f\"\\nIteration #{adversarial_iterations}\")\n",
        "    print(f\"Current solution: \")\n",
        "    for c in chips:\n",
        "        print(f\"x['{c}']= {x[c]:.2f}\")\n",
        "\n",
        "    # Pessimization\n",
        "    worst_z, constraint_violation = BIMPessimization(x, delta, gamma)\n",
        "\n",
        "    # If pessimization yields no violation, stop the procedure, otherwise add a scenario and repeat\n",
        "    if constraint_violation < stopping_precision:\n",
        "        print(\"No violation found. Stopping the procedure.\")\n",
        "        adversarial_converged = True\n",
        "    else:\n",
        "        print(\n",
        "            f\"Violation found: z['logic'] = {worst_z['logic']},  z['memory'] = {worst_z['memory']}, \"\n",
        "            f\"constraint violation: {constraint_violation:6.2f}\"\n",
        "        )\n",
        "        Z.append(worst_z)\n",
        "\n",
        "    adversarial_iterations += 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It takes only two scenarios to be added to the baseline scenario to arrive at the solution which is essentially robust! For that reason, in many settings the adversarial approach is very viable. In fact, because the budgeted uncertainty set for two uncertain parameters has at most 8 vertices, we are guaranteed that it would never take more than 8 iterations to reach a fully robust solution (constraint violation of exactly $0$).\n",
        "\n",
        "This is not true, however, if the uncertainty set is not a polytope, but is, for example, an ellipsoid (ball) with infinitely many extreme points - it is expected that there will always be some minuscule constraint violation remaining after a certain number of iterations. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We will now illustrate how to use conic optimization to solve the problem using robust counterparts for an ellipsoidal uncertainty set."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FeH2kXz6K3iJ"
      },
      "source": [
        "## Ball uncertainty set\n",
        "\n",
        "Let us now make yet another different assumption regarding the uncertainty related to copper consumption. More specifically, we assume that the two uncertain coefficients $z_1$ and $z_2$ can vary in a 2-dimensional ball centered around the point $(\\bar{z}_1,\\bar{z}_2) = (4,2)$ and with radius $r$. \n",
        "\n",
        "### Robust counterpart of ball uncertainty\n",
        "A straightforward reformulation leads to the equivalent constraint:\n",
        "\n",
        "$$\n",
        "  \\bar{z}_1x_1+\\bar{z}_2x_2 + r \\|x\\|_2 \\leq 4800\n",
        "$$\n",
        "\n",
        "By defining $y = 4800 - \\bar{z}_1x_1 - \\bar{z}_2x_2$ and $w = r x$, we may write:\n",
        "\n",
        "$$\n",
        "  \\|w\\|^2_2 \\leq y^2\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PdNL7TLNB18o"
      },
      "source": [
        "We now need to add this newly obtained conic constraint to the original BIM model. The optimization problem is nonlinear, but dedicated solvers can leverage the fact that it is conic and solve it efficiently. Specifically, `cplex`, `gurobi`, `xpress`, `copt`, and `mosek` support second-order cones. On the other hand, `ipopt` is a generic solver for nonlinear optimization problems.\n",
        "\n",
        "Note that $\\| x \\| \\leq t$ is for $t \\geq 0$ equivalent to $\\| x \\|^2 \\leq t^2$. A few commercial solvers (`gurobi`, `cplex`, `xpress`, and `copt`) auto-detect second-order cones from quadratic inequalities. AMPL Mosek driver [recognizes conic algebra in the model](https://amplmp.readthedocs.io/en/latest/rst/model-guide.html) and presents it to Mosek via its API. Note that the essential part to make the model convex is having the right-hand side nonnegative."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Overwriting BIM_robust_ball.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile BIM_robust_ball.mod\n",
        "\n",
        "set CHIPS;\n",
        "\n",
        "param profits{CHIPS};\n",
        "param copper{CHIPS};\n",
        "\n",
        "var x{CHIPS} >= 0;\n",
        "\n",
        "maximize Profit: sum {c in CHIPS} profits[c] * x[c];\n",
        "\n",
        "s.t. Silicon: x['logic'] <= 1000;\n",
        "s.t. Germanium: x['memory'] <= 1500;\n",
        "s.t. Plastic: sum {c in CHIPS} x[c] <= 1750;\n",
        "\n",
        "param radius;\n",
        "    \n",
        "var y >= 0;\n",
        "var w{CHIPS} >= 0;\n",
        "\n",
        "s.t. Copper:\n",
        "    y == 4800 - sum {c in CHIPS} copper[c] * x[c];\n",
        "s.t. X2W{i in CHIPS}:\n",
        "    w[i] == radius * x[i];\n",
        "s.t. Robust:\n",
        "    y^2 >= sum {c in CHIPS} w[c]^2;\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [],
      "source": [
        "def BIMWithBallUncertainty(radius, SOLVER, int_x=False):\n",
        "    ampl = AMPL()\n",
        "    ampl.read(\"BIM_robust_ball.mod\")\n",
        "    if int_x:\n",
        "        ampl.eval(\"redeclare var x{CHIPS} >= 0, integer;\")\n",
        "\n",
        "    ampl.set[\"CHIPS\"] = chips\n",
        "    ampl.param[\"profits\"] = profits\n",
        "    ampl.param[\"copper\"] = copper\n",
        "\n",
        "    ampl.param[\"radius\"] = radius\n",
        "\n",
        "    ampl.option[\"solver\"] = SOLVER\n",
        "    ampl.solve()\n",
        "\n",
        "    return ampl"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "executionInfo": {
          "elapsed": 29,
          "status": "ok",
          "timestamp": 1633441689060,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "RB17G1AqK3iK",
        "outputId": "8f2d5c93-bb47-4574-a4d5-15a2f4cc6c54"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Ipopt 3.12.13: \n",
            "\n",
            "******************************************************************************\n",
            "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
            " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
            "         For more information visit http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "This is Ipopt version 3.12.13, running with linear solver mumps.\n",
            "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
            "\n",
            "Number of nonzeros in equality constraint Jacobian...:        7\n",
            "Number of nonzeros in inequality constraint Jacobian.:        5\n",
            "Number of nonzeros in Lagrangian Hessian.............:        3\n",
            "\n",
            "Total number of variables............................:        5\n",
            "                     variables with only lower bounds:        3\n",
            "                variables with lower and upper bounds:        2\n",
            "                     variables with only upper bounds:        0\n",
            "Total number of equality constraints.................:        3\n",
            "Total number of inequality constraints...............:        2\n",
            "        inequality constraints with only lower bounds:        1\n",
            "   inequality constraints with lower and upper bounds:        0\n",
            "        inequality constraints with only upper bounds:        1\n",
            "\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "   0 -2.0999979e-01 4.80e+03 1.68e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
            "   1 -1.5068986e+04 9.09e-13 1.26e+05  -1.0 1.37e+03    -  1.08e-05 1.00e+00f  1\n",
            "   2 -1.5401654e+04 0.00e+00 4.25e+04  -1.0 1.11e+02   2.0 6.57e-01 1.00e+00f  1\n",
            "   3 -1.5551016e+04 9.09e-13 1.15e+04  -1.0 4.99e+01   1.5 9.84e-01 1.00e+00f  1\n",
            "   4 -1.5602002e+04 9.09e-13 2.22e+03  -1.0 1.70e+01   1.0 1.00e+00 1.00e+00f  1\n",
            "   5 -1.5611246e+04 0.00e+00 1.06e+02  -1.0 2.56e+00   0.6 1.00e+00 1.00e+00h  1\n",
            "   6 -1.5616306e+04 0.00e+00 2.01e+00  -1.0 1.62e+00   0.1 1.00e+00 1.00e+00f  1\n",
            "   7 -1.7601149e+04 1.36e+03 1.93e+00  -1.0 1.70e+04    -  4.97e-03 3.89e-02f  1\n",
            "   8 -1.7620596e+04 1.36e+03 1.93e+00  -1.0 2.53e+04    -  2.25e-02 2.67e-04f  1\n",
            "   9 -1.7620526e+04 1.34e+03 4.92e+00  -1.0 5.25e+02    -  1.00e+00 9.75e-03h  1\n",
            "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
            "  10 -1.7601097e+04 0.00e+00 4.69e-01  -1.0 1.29e+01    -  1.00e+00 1.00e+00h  1\n",
            "  11 -1.7603063e+04 7.11e-15 9.83e-03  -1.0 5.16e+00    -  1.00e+00 1.00e+00h  1\n",
            "  12 -1.7603064e+04 0.00e+00 1.00e-06  -1.0 1.62e+00    -  1.00e+00 1.00e+00h  1\n",
            "  13 -1.7603259e+04 3.55e-15 2.90e-06  -2.5 8.31e+00    -  1.00e+00 1.00e+00f  1\n",
            "  14 -1.7603264e+04 0.00e+00 1.50e-09  -3.8 2.12e-01    -  1.00e+00 1.00e+00h  1\n",
            "  15 -1.7603265e+04 7.11e-15 1.84e-11  -5.7 1.26e-02    -  1.00e+00 1.00e+00h  1\n",
            "  16 -1.7603265e+04 0.00e+00 2.51e-14  -8.6 1.57e-04    -  1.00e+00 1.00e+00h  1\n",
            "\n",
            "Number of Iterations....: 16\n",
            "\n",
            "                                   (scaled)                 (unscaled)\n",
            "Objective...............:  -1.7603264635190098e+04   -1.7603264635190098e+04\n",
            "Dual infeasibility......:   2.5059815333960955e-14    2.5059815333960955e-14\n",
            "Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00\n",
            "Complementarity.........:   2.5059819139477092e-09    2.5059819139477092e-09\n",
            "Overall NLP error.......:   2.5059819139477092e-09    2.5059819139477092e-09\n",
            "\n",
            "\n",
            "Number of objective function evaluations             = 17\n",
            "Number of objective gradient evaluations             = 17\n",
            "Number of equality constraint evaluations            = 17\n",
            "Number of inequality constraint evaluations          = 17\n",
            "Number of equality constraint Jacobian evaluations   = 17\n",
            "Number of inequality constraint Jacobian evaluations = 17\n",
            "Number of Lagrangian Hessian evaluations             = 16\n",
            "Total CPU secs in IPOPT (w/o function evaluations)   =      0.011\n",
            "Total CPU secs in NLP function evaluations           =      0.000\n",
            "\n",
            "EXIT: Optimal Solution Found.\n",
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b \n",
            "Ipopt 3.12.13: Optimal Solution Found\n",
            "\n",
            "suffix ipopt_zU_out OUT;\n",
            "suffix ipopt_zL_out OUT;\n",
            "Solver: ipopt, solver status: solve_result\n",
            "  'solved'  \n",
            "\n",
            "x = ({'logic': 617.7548258979735, 'memory': 1132.245191601602})\n",
            "optimal value = 17603.26\n"
          ]
        }
      ],
      "source": [
        "radius = 0.05\n",
        "ampl = BIMWithBallUncertainty(radius, SOLVER_NLO)\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "print(f\"Solver: {SOLVER_NLO}, solver status:\", ampl.solve_result)\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CGAcVL5yK3iK"
      },
      "source": [
        "The solvers `bonmin`, `cplex`, `gurobi` and `xpress` are capable of solving the mixed integer version of the same model: "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "executionInfo": {
          "elapsed": 526,
          "status": "ok",
          "timestamp": 1633441689559,
          "user": {
            "displayName": "Joaquim Gromicho",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
            "userId": "14375950305363805729"
          },
          "user_tz": -120
        },
        "id": "WGJvS_K_K3iK",
        "outputId": "556705bc-5883-4c02-b6dd-394cfbc5e969"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Bonmin 1.8.9 using Cbc 2.10.8 and Ipopt 3.12.13\n",
            "bonmin: \n",
            "\n",
            "******************************************************************************\n",
            "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
            " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
            "         For more information visit http://projects.coin-or.org/Ipopt\n",
            "******************************************************************************\n",
            "\n",
            "NLP0012I \n",
            "              Num      Status      Obj             It       time                 Location\n",
            "NLP0014I             1         OPT -17603.265       16 0.035354\n",
            "NLP0014I             2         OPT -17602.552        7 0.007343\n",
            "NLP0014I             3         OPT -17601       10 0.009459\n",
            "NLP0014I             4         OPT -17601        7 0.005379\n",
            "NLP0014I             5         OPT -17601.863        7 0.00515\n",
            "Cbc0010I After 0 nodes, 1 on tree, 1e+50 best solution, best possible -1.7976931e+308 (0.03 seconds)\n",
            "NLP0014I             6         OPT -17601.863        7 0.006115\n",
            "NLP0014I             7         OPT -17601        7 0.006989\n",
            "NLP0014I             8      INFEAS 0.4853767       14 0.016151\n",
            "NLP0014I             9         OPT -17599.648        7 0.005641\n",
            "NLP0014I            10         OPT -17595        9 0.006713\n",
            "NLP0012I \n",
            "              Num      Status      Obj             It       time                 Location\n",
            "NLP0014I             1         OPT -17595        1 0.00125\n",
            "Cbc0004I Integer solution of -17595 found after 44 iterations and 5 nodes (0.08 seconds)\n",
            "NLP0014I            11         OPT -17601       11 0.008915\n",
            "NLP0014I             2         OPT -17601        1 0.001178\n",
            "Cbc0004I Integer solution of -17601 found after 55 iterations and 6 nodes (0.09 seconds)\n",
            "Cbc0001I Search completed - best objective -17601, took 55 iterations and 6 nodes (0.09 seconds)\n",
            "Cbc0032I Strong branching done 2 times (31 iterations), fathomed 0 nodes and fixed 0 variables\n",
            "Cbc0035I Maximum depth 2, 0 variables fixed on reduced cost\n",
            "\n",
            " \t\"Finished\"\n",
            "\n",
            "bonmin: Optimal\n",
            "Solver: bonmin, solver status: solve_result\n",
            "  'solved'  \n",
            "\n",
            "x = ({'logic': 617.0, 'memory': 1133.0})\n",
            "optimal value = 17601.00\n"
          ]
        }
      ],
      "source": [
        "ampl = BIMWithBallUncertainty(radius, SOLVER_MINLO, True)\n",
        "\n",
        "x = ampl.get_variable(\"x\").to_dict()\n",
        "print(f\"Solver: {SOLVER_MINLO}, solver status:\", ampl.solve_result)\n",
        "print(f\"x = ({x})\")\n",
        "print(f'optimal value = {ampl.obj[\"Profit\"].value():.2f}')"
      ]
    }
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