Question

Find the maximum value of Z = 7x + 7y, subject to the constraints

x ≥ 0, y ≥ 0, x + y ≥ 2 and 2x + 3y ≤ 6.

Answer 1

It is given that

Z = 7x + 7y, subject to the constraints

x ≥ 0, y ≥ 0, x + y ≥ 2 and 2x + 3y ≤ 6

Draw the line x + y = 2 and 2x + 3y = 6 and shaded region which is satisfied by above inequalities

We know that the feasible region is bounded

A (2, 0), B (3, 0) and C (0, 2) are the corner points

So the value of Z at A (3, 0)

Z = 7 × 2 + 7 × 0 = 14

Value of Z at B (3, 0)

Z = 7 × 3 + 7 × 0 = 21

Value of Z at C (0, 2)

Z = 7 × 0 + 7 × 2 = 14

Hence, the maximum value of Z is 21 which occurs at B (3, 0).