Given that 36x_{1} + 6x_{2} ≥ 108

**Let 36x**_{1} + 6x_{2} = 108

6x_{1} + x_{2} = 18

Also given that 3x_{1} + 12x_{2} ≥ 36

**Let 3x**_{1} + 12x_{2} = 36

x_{1} + 4x_{2} = 12

Also given that 20x_{1} + 10x_{2} ≥ 100

**Let 20x**_{1} + 10x_{2} = 100

2x_{1} + x_{2} = 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 x**_{1} = 4, x_{2} = 2 and Z_{min} = 160