$ondollar title Clever Clyde (LP) Example 5.2 of Rardin (1998)

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

scalar alpha "fraction of the company from investor 2";

free variable compsize "company size";

positive variables
x1  "from investor 1 (000)",
x2  "from investor 2 (000)",
x3  "from clyde";

equations
obj    "maxmize company size",
min100 "total at least 100",
half1  "half from investor 1",
alph2  "alpha from investor 2",
clyde  "clyde limit of 5";

obj..
compsize =e= x1 + x2 +x3;

min100..
x1 + x2 +x3 =g= 100;

half1..
x1 =e= 0.50 * (x1 + x2 + x3);

alph2..
x2 =e= alpha * (x1 + x2 + x3);

clyde..
x3 =l= 5;

model clevclyd /all/;

alpha = 0.40;
solve clevclyd using lp maximizing compsize;

alpha = 0.49;
solve clevclyd using lp maximizing compsize;

alpha = 0.50;
solve clevclyd using lp maximizing compsize;