$ondollar title DClub (NLP) Example 3.1 of Rardin (1998)

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

set p "populations" /1*3/;

parameter popl(p) "population of p (000)"
/1 60, 2 20, 3 30/;

parameter px1(p) "population x1 coordinate for p"
/1 -1, 2 1, 3 0/;

parameter px2(p) "population x2 coordinate for p"
/1 3, 2 3, 3 -4/;

free variables
patron "total patronage",
x1     "store x1 coordinate",
x2     "store x2 coordinate";

equations
obj      "maximize total patronage"
avoid(p) "avoid downtown p";

obj..
patron =e= sum(p, popl(p)/( 1 + sqr(x1 - px1(p)) + sqr(x2 -px2(p)) ) );

avoid(p)..
sqr(x1 - px1(p)) + sqr(x2 - px2(p)) =g= 0.25;

model dclub /all/;

x1.l = -5.0;
x2.l = 0.0;

solve dclub using nlp maximizing patron;

x1.l = 0.0;
x2.l = 3.5;

solve dclub using nlp maximizing patron;

x1.l = -.5;
x2.l = -3.0;

solve dclub using nlp maximizing patron;