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