Question

The maximum value of z = 6x + 8y subject to constraints 2x + y ≤ 30, x + 2y ≤ 24 and x ≥ 0, y ≥ 0 is ______.

Options

• 90

• 120

• 96

• 240

Answer 1

The maximum value of z = 6x + 8y subject to constraints 2x + y ≤ 30, x + 2y ≤ 24 and x ≥ 0, y ≥ 0 is 120.

Explanation:

Here, 2x + y ≤ 30, x + 2y ≤ 24, x, y ≥ 0

The shaded region represents the feasible region, hence z = 6x + 8y.

Obviously it is maximum at (12, 6).

Hence z = 12 × 6 + 8 × 6 = 120