Given that 36x1 + 6x2 ≥ 108
Let 36x1 + 6x2 = 108
6x1 + x2 = 18
Also given that 3x1 + 12x2 ≥ 36
Let 3x1 + 12x2 = 36
x1 + 4x2 = 12
Also given that 20x1 + 10x2 ≥ 100
Let 20x1 + 10x2 = 100
2x1 + x2 = 10
The feasible region satisfying all the conditions is ABCD.
The co-ordinates of the comer points are A(12, 0), B(4, 2), C(2, 6) and D(0, 18).
The minimum value of Z occurs at B(4, 2)
∴ The optimal solution is x1 = 4, x2 = 2 and Zmin = 160