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
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1620
For a bounded feasible region, the maximum and minimum of Z occur at corner points. Evaluating \(Z = 30x + 20y\) at each:
\(Z(15, 0) = 450\)
\(Z(40, 0) = 1200\)
\(Z(4, 18) = 120 + 360 = 480\)
\(Z(6, 12) = 180 + 240 = 420\)
So the maximum is 1200 at (40, 0) and the minimum is 420 at (6, 12):
\(1200 + 420 = 1620\)