set PROD;   # products
set STAGE;  # stages

param rate {PROD,STAGE} > 0; # tons per hour in each stage
param avail {STAGE} >= 0;    # hours available/week in each stage
param profit {PROD};         # profit per ton

param commit {PROD} >= 0;    # lower limit on tons sold in week
param market {PROD} >= 0;    # upper limit on tons sold in week

var Make {p in PROD} >= commit[p], <= market[p]; # tons produced

maximize Total_Profit: sum {p in PROD} profit[p] * Make[p];

               # Objective: total profits from all products

subject to Time {s in STAGE}:
   sum {p in PROD} (1/rate[p,s]) * Make[p] <= avail[s];

               # In each stage: total of hours used by all
               # products may not exceed hours available