Question

The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function is Z = ax + 2by where a, b > 0. The condition on a and b such that the maximum Z occurs at Q and S is ______.

Options

• a – 5b = 0

• a – 3b = 0

• a – 2b = 0

• a – 8b = 0

Answer 1

The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function is Z = ax + 2by where a, b > 0. The condition on a and b such that the maximum Z occurs at Q and S is a – 8b = 0.

Explanation:

Given, Max. Z = ax + 2by

Max. value of Z on Q(3, 5) = Max. value of Z on S(4, 1)

`\implies` 3a + 10b = 4a + 2b

`\implies` a – 8b = 0