If the corner points of the bounded feasible region of an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of objective function $F= 4x + 6y$ occurs at
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → every point on the line segment joining (0, 2) and (3, 0)
Objective function: $F = 4x + 6y$
Corner points:
(0, 2): F = 4*0 + 6*2 = 12
(3, 0): F = 4*3 + 6*0 = 12
(6, 0): F = 4*6 + 6*0 = 24
(6, 8): F = 4*6 + 6*8 = 24 + 48 = 72
(0, 5): F = 4*0 + 6*5 = 30
The minimum value F = 12 occurs at (0, 2) and (3, 0).
Since the objective function is linear, all points on the line segment joining (0, 2) and (3, 0) will also give F = 12.