Question

The maximum value of z = 6x + 8y subject to x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0 is ______.

Options

• 72

• 42

• 96

• 24

Answer 1

The maximum value of z = 6x + 8y subject to x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0 is 72.

Explanation:

We have, z = 6x + 8y

subject to constrants x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0.

On taking given constraints as equations,

we get the following graph

Intersecting point of the line x- y = 0 and x + 3y = 12 is 8(3, 3).

Here, OABO is the required feasible region

Whose corner points are 0(0, 0), A (12, 0) and B(O, 4)

Now, 

Corner points	Z = 6x + 8y
O(0, 0)	6 × 0 + 8 × 0 = 0
A(12, 0)	6 × 12 + 8 × 0 = 72 (maximum)
B(3, 3)	6 × 3 + 8 × 3 = 42

∴ Maximum value of Z is 72.