min: -x1 - 2 x2 + 0.1 x3 + 3 x4; r_1: +x1 +x2 <= 5; r_2: +2 x1 -x2 >= 0; r_3: -x1 +3 x2 >= 0; r_4: +x3 +x4 >= 0.5; x3 >= 1.1; int x3, x4;