If the corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 2), (3, 0), (6, 0), (6, 8) and (0,5), then which of the following are correct for the objective function $Z = 4x + 6y$?

(A) The minimum value of the objective function occurs at (0, 2) and (3, 0) only.
(B) The minimum value of the objective function occurs at the mid-point of the line segment joining the points (0, 2) and (3, 0) only.
(C) The minimum value of the objective function occurs at every point of the line segment joining the points (0, 2) and (3, 0).
(D) The difference between the maximum value and minimum value of the objective function is 60.

Choose the correct answer from the options given below:

(C) and (D) only

The correct answer is Option (4) → (C) and (D) only

Objective function: $Z = 4x + 6y$

Evaluate $Z$ at each corner point:

(0,2): $Z = 4*0 + 6*2 = 12$

(3,0): $Z = 4*3 + 6*0 = 12$

(6,0): $Z = 4*6 + 6*0 = 24$

(6,8): $Z = 4*6 + 6*8 = 24 + 48 = 72$

(0,5): $Z = 4*0 + 6*5 = 30$

Minimum value: $12$ at points (0,2) and (3,0)

Since objective function is linear, the minimum occurs at every point on the line segment joining these two points.

Maximum value: $72$ at (6,8)

Difference between maximum and minimum: $72 - 12 = 60$

Answer: (C) and (D)