$ondollar title Top Brass (LP) Example 5.1 of Rardin (1998)  (modified)

$offsymxref offsymlist offuelxref offuellist offupper
option limrow = 0, limcol = 0;

set I/football, soccer/;

free variable profit "total profit";

positive variables
x(I) "trophies";

parameters
         profitMargin(I) / "football" 12 , "soccer" 9 /
         boardFeet(I)    / "football"  4 , "soccer" 2 /
         plaques(I)      / "football"  1 , "soccer" 1 /;

scalar
         plaquesMax /1750/
         woodMax    /4800/;

equations
obj    "max total profit"
foot   "brass footballs"
socc   "brass soccer balls",
plaq   "brass plaques",
wood   "bdft wood";

obj..
profit =e= sum(I, profitMargin(I)*x(I));

foot..
x("football") =l= 1000;

socc..
x("soccer") =l= 1500;

plaq..
sum(I,plaques(I)*x(I)) =l= plaquesMax;

wood..
sum(I,boardFeet(I)*x(I)) =l= woodMax;

model topbrass /all/;

solve topbrass using lp maximizing profit;