//use the specialized module for Linear Multiplicative Programs
MODULE: LMP;

INTEGER_VARIABLES x1, x2, x3;
POSITIVE_VARIABLES x4;

LOWER_BOUNDS {
x1: 0;
x2: 0;
x3: 0;
}

UPPER_BOUNDS{
x1: 100;
x2: 100;
x3: 100;
x4: 100;
}


EQUATIONS e1, e2, e3, e4;

e1 : -88*x1-x2-15*x3-82*x4 <= -6;
e2 : -30*x1-25*x2-83*x3-68*x4 <= -6;
e3 : -59*x1-72*x3-29*x4 <= -3;
e4 : -17*x1-35*x2-57*x3-24*x4 <= -3;

OBJ : minimize  (2+7*x1+9*x2+8*x3+8*x4)*(9+9*x2+5*x3+4*x4)*(6+3*x1+8*x2+3*x3+8*x4);