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# Page 15
# products
set PROD := { "bands", "coils", "plate" };
# stages
set STAGE := { "reheat", "roll" };
# tons per hour in each stage
param rate[PROD * STAGE] :=
<"bands","reheat"> 200,
<"bands","roll"> 200,
<"coils","reheat"> 200,
<"coils","roll"> 140,
<"plate","reheat"> 200,
<"plate","roll"> 160;
# profit per ton
param profit[PROD] := <"bands"> 25, <"coils"> 30, <"plate"> 29;
# lower limit on tons sold in week
param commit[PROD] := <"bands"> 1000, <"coils"> 500, <"plate"> 750;
# upper limit on tons sold in week
param market[PROD] := <"bands"> 6000, <"coils"> 4000, <"plate"> 3500;
# hours available/week in each stage
param avail[STAGE] := <"reheat"> 35, <"roll"> 40;
# tons produced
var Make[<p> in PROD] real >= commit[p] <= market[p]; # tons produced
# Objective: total profits from all products
maximize total_profit: sum <p> in PROD : profit[p] * Make[p];
# In each stage: total of hours usd by all
# products may not exceed hour available
subto Time: forall <s> in STAGE :
sum <p> in PROD : (1/rate[p,s]) * Make[p] <= avail[s];
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