$ondollar title Indy Car (ILP) Example 11.1 of Rardin (1998)

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

set j "proposed features" /1*6/;

parameter c(j)  "cost of feature j (000)"
/1 10.2, 2 6.0, 3 23.0, 4 11.1, 5 9.8, 6 31.6/;

parameter m(j)  "mph increase with feature j"
/1 8, 2 3, 3 15, 4 7, 5 10, 6 12/;

free variables
mph  "mph gain",
cost "total cost";

binary variables
x(j) "if feature j selected";

equations
totcost  "total cost",
totmph   "total mph",
budget   "cost limit",
mphreq   "mph requirement";

totcost..
cost =e= sum(j, c(j)*x(j));

totmph..
mph =e= sum(j, m(j)*x(j));

budget..
sum(j, c(j)*x(j)) =l= 35;

mphreq..
sum(j, m(j)*x(j)) =g= 30;

model maxversion /totmph, budget/;

solve maxversion using mip maximizing mph;

model minversion /totcost, mphreq/;

solve minversion using mip minimizing cost;