The corner points of the bounded feasible region determined by the system of linear constraints are (15, 0), (40, 0), (4, 18) and (6, 12). If objective function is $Z= 30x +20y$, then the sum of the maximum and the minimum values of Z is

1620

The correct answer is Option (3) → 1620

Objective function: $Z = 30x + 20y$

Evaluate $Z$ at each corner point:

At (15, 0): $Z = 30 \cdot 15 + 20 \cdot 0 = 450$

At (40, 0): $Z = 30 \cdot 40 + 20 \cdot 0 = 1200$

At (4, 18): $Z = 30 \cdot 4 + 20 \cdot 18 = 120 + 360 = 480$

At (6, 12): $Z = 30 \cdot 6 + 20 \cdot 12 = 180 + 240 = 420$

Maximum value of $Z$ = 1200

Minimum value of $Z$ = 420

Sum of maximum and minimum values = 1200 + 420 = 1620