$ondollar title Highway Patrol (LP) Example 4.7 of Rardin (1998)

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

set j "highway segments" /1*8/;

parameter u(j) "upper bound for hiway segment j"
/1 4, 2 8, 3 5, 4 7, 5 6, 6 5, 7 6, 8 4/;

parameter r(j) "reduction potential on hiway segment j"
/1 11, 2 3, 3 4, 4 14, 5 2, 6 19, 7 10, 8 13/;

free variable objval;

positive variable x(j) "number of officer on hiway segment j";
x.up(j) = u(j);

equations
maxisum    "maximize the total reduction",
maximin(j) "minimum less that reduction on j",
avail      "total available officers" ;

maxisum..
objval =e= sum(j, r(j)*x(j));

maximin(j)..
objval =l= r(j)*x(j);

avail..
sum(j, x(j)) =l= 25;

model sumvers /maxisum, avail/;

solve sumvers using lp maximizing objval;

model maxminvers /maximin, avail/;
 
solve maxminvers using lp maximizing objval;