var y1 >=0;
var y2 >=0;
var y3 >=-infinity;

minimize cost: 4*y1 + 4*y2 + 6*y3;

subto constraint1: y1 + y3 >= 4;
subto secondConstraint: y1+y2+y3 >= 5;
subto blah: 2*y2+y3 >= 6;
subto anotherconst: y3 >= 3;