Question

Maximize Z = 2x + 3y, subject to the constraints

x ≥ 0, y ≥ 0, x + 2y ≥ 1 and x + 2y ≤ 10.

Answer 1

It is given that

Z = 2x + 3y, subject to the constraints

x ≥ 0, y ≥ 0, x + 2y ≥ 1 and x + 2y ≤ 10

Draw the line x + 2y = 1 and x + 2y = 10 and shaded region which is satisfied by above inequalities

We know that the feasible region is bounded

A (1, 0), B (10, 0), C (0, 5) and D (0, 1/2) are the corner points

So the value of Z at A (1, 0)

Z = 2

Value of Z at B (10, 0)

Z = 20

Value of Z at C (0, 5)

Z = 15

Value of Z at D (0, 1/2)

Z = 3/2

Hence, the maximum value of Z is 3/2 which occurs at A (0, 1/2).