The corner points of the feasible region of an LPP are (0, 0), (30, 0), (20, 30) and (0, 50). If the objective function maximize (z) = ax + by, where a ≠ b and a, b > 0, has alternate optimal solutions, then

a = 2b a = 3b 2a = b 3a = b

a = 3b

Corner points       Z = ax + by   (0, 0)  Z(0, 0) = 0  (30, 0)  Z(30, 0) = 30a   (0, 50)  Z(0, 50) = 50b  (20, 30)  Z(20, 30) = 20a + 30 b  for only 20a + 30b = 30a ⇒ a = 3b → options match solution So Option B.