Question

For an objective function Z = ax + by, where a, b > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:

Options

• b − 3a = 0

• a = 3b

• a + 2b = 0

• 2a − b = 0

Answer 1

b − 3a = 0

Explanation:

As Z is maximum at (30, 30) and (0, 40)

⇒ 30a + 30b = 40b

⇒ b − 3a = 0