Question

The solution for maximizing the function z = x + 2y under a LPP with constraints x + y ≥ 1, x + 2y ≤ 10, y ≤ 3 and x, y ≥ 0, is ______ 

Options

• x = 0, y = 0, z = 0

• x = 3, y = 3, z = 6

• There are infinitely many solutions.

• None of these

Answer 1

The solution for maximizing the function z = x + 2y under a LPP with constraints x + y ≥ 1, x + 2y ≤ 10, y ≤ 3 and x, y ≥ 0, is There are infinitely many solutions.

Explanation:

The corner points of feasible region are

A(1, 0), B(10, 0), C(4, 3), D(0, 3) and E(0, 1)

At A (1, 0), z = 1

At B (10, 0), z = 10

At C (4, 3), z = 10

At D (0, 3), z = 6

At E (0, 1), z = 2

z has maximum value at both B (10, 0) and C (4, 3).

∴  z has infinite solutions on seg BC.