Minimize
obj: y_1 + y_2 + y_3

Subject To
c1: y_1 + y_2 + y_3 >= 1
c2: x_1_1 + 3 x_2_1 + x_3_1 - 5 y_1<= 0
c3: x_1_2 + 3 x_2_2 + x_3_2 - 3 y_2 <= 0
c4: x_1_3 + 3 x_2_3 + x_3_3 - 3 y_3 <= 0
c5: x_1_1 + x_1_2 + x_1_3 = 1
c6: x_2_1 + x_2_2 + x_2_3 = 1
c7: x_3_1 + x_3_2 + x_3_3 = 1
Bounds
0 <= y_1 <= 1
0 <= y_2 <= 1
0 <= y_3 <= 1
0 <= x_1_1 <= 1
0 <= x_1_2 <= 1
0 <= x_1_3 <= 1
0 <= x_2_1 <= 1
0 <= x_2_2 <= 1
0 <= x_2_3 <= 1
0 <= x_3_1 <= 1
0 <= x_3_2 <= 1
0 <= x_3_3 <= 1
End