If the objective function for a linear programming problem (LPP) is $Z = 4x + 5y$ and the corner points of the bounded feasible region are (9, 0), (4, 3), (2, 5), and (0, 8), then the minimum value of Z is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 31
Objective function: $Z = 4x + 5y$
Evaluate $Z$ at each corner point:
(9,0): $Z = 4*9 + 5*0 = 36$
(4,3): $Z = 4*4 + 5*3 = 16 + 15 = 31$
(2,5): $Z = 4*2 + 5*5 = 8 + 25 = 33$
(0,8): $Z = 4*0 + 5*8 = 40$
Minimum value of $Z = 31$ at point (4,3)