param a{1..12};

var
   x {1..5};
param best_val_found := -30665.53867;
param eps := 1; 		# = max(1, 1% x best_val_found)

subject to f:
        5.3578547*x[3]^2 + 0.8356891*x[1]*x[5] + 37.293239*x[1] - 40792.141 <= best_val_found + eps;
subject to
cons1:         x[1] >= 78;
cons2:         x[1] <= 102;
cons3:         x[2] >= 33;
cons4:         x[2] <= 45;
cons5 {i in 3..5}: x[i] >= 27;
cons6 {i in 3..5}: x[i] <= 45;
cons7:         92 >= a[1] + a[2]*x[2]*x[5] + a[3]*x[1]*x[4] - a[4]*x[3]*x[5];
cons8:         a[1] + a[2]*x[2]*x[5] + a[3]*x[1]*x[4] - a[4]*x[3]*x[5] >= 0;
cons9:         110 >=  a[5] + a[6]*x[2]*x[5] + a[7]*x[1]*x[2] + a[8]*x[3]^2;
cons10:         a[5] + a[6]*x[2]*x[5] + a[7]*x[1]*x[2] + a[8]*x[3]^2 >= 90;
cons11:         25 >= a[9] + a[10]*x[3]*x[5] + a[11]*x[1]*x[3] + a[12]*x[3]*x[4];
cons12:         a[9] + a[10]*x[3]*x[5] + a[11]*x[1]*x[3] + a[12]*x[3]*x[4] >= 20;

data;
param a := 
1        85.334407
2        0.0056858
3        0.0006262
4        0.0022053
5        80.51249
6        0.0071317
7        0.0029955
8        0.0021813
9        9.300961
10        0.0047026
11        0.0012547
12        0.0019085;
             
solve;
display x;