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

every point on the line segment joining (0, 2) and (3, 0)

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.