set PROD;  # products

param rate {PROD} > 0;     # produced tons per hour
param avail >= 0;          # hours available in week
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: sum {p in PROD} (1/rate[p]) * Make[p] <= avail;

               # Constraint: total of hours used by all
               # products may not exceed hours available