Question

The maximum value of z = 7x + 6y.
Subject to the constraints x ≤ 45, y ≤ 55 and x ≥ 0, y ≥ 0 is ______.

Options

• 654

• 315

• 330

• 645

Answer 1

The maximum value of z = 7x + 6y.
Subject to the constraints x ≤ 45, y ≤ 55 and x ≥ 0, y ≥ 0 is 645.

Explanation:

The feasible region lies on the origin side of both lines.

The comer points of feasible region are

O (0, 0), A (45, 0), B (0, 55) and P (45, 55)

∴ At O (0, 0), z = 0

At A (45, 0), z = 315

At B (0, 55), z = 330

At P (45, 55), z = 645

∴ The maximum value of z is 645.