Given that 3x_{1} + x_{2} ≤ 9

**Let 3x**_{1} + x_{2} = 9

Also given that x_{1} + 2x_{2} ≤ 8

**Let x**_{1} + 2x_{2} = 8

3x_{1} + x_{2} = 9 … (1)

x_{1} + 2x_{2} = 8 … (2)

(1) x 2 ⇒ 6x_{1} + 2x_{2} = 18 ... (3)

(2) + (3) ⇒ -5x_{1} = -10

x_{1} = 2

**x**_{1} = 2 substitute in (1)

3(2) + x_{2} = 9

x_{2} = 3

The feasible region satisfying all the conditions is OABC.

The co-ordinates of the corner points are O(0, 0), A(3, 0), B(2, 3), C(0, 4)

The maximum value of Z occurs at (2, 3).

**∴ The optimal solution is x**_{1} = 2, x_{2} = 3 and Z_{max} = 230