The corner points of the feasible region determined by a system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). If the objective function is \(Z=4x+3y\), then which one of the following is true?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Max. \(Z \lt 400\)
The maximum of Z over the feasible region is the largest of its values at the corner points:
\(Z(0, 0) = 0\)
\(Z(0, 40) = 0 + 120 = 120\)
\(Z(20, 40) = 80 + 120 = 200\)
\(Z(60, 20) = 240 + 60 = 300\)
\(Z(60, 0) = 240 + 0 = 240\)
So Max. Z = 300, at (60, 20), which is less than 400.