In a linear programming problem, the objective function \(Z = 5x + 4y\) is to be maximised, and the point (2, 3) lies in the feasible region. If Z has a maximum value on the feasible region, then this maximum value
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → cannot be less than 22
At the feasible point (2, 3),
\(Z = 5(2) + 4(3) = 22\)
The maximum value is the largest value of Z over all feasible points, so it is at least the value at any one feasible point. Hence it cannot be less than 22.
Why the other options are incorrect
Option (1) must be equal to 22 — Incorrect. Another feasible point may give a larger value; for the region \(x + y \le 10\), \(x, y \ge 0\), the maximum is 50.
Option (2) cannot be more than 22 — Incorrect. The same example has maximum 50, which is more than 22.
Option (3) must be more than 22 — Incorrect. (2, 3) may itself be the optimal point; for the region \(x \le 2\), \(y \le 3\), \(x, y \ge 0\), the maximum is exactly 22.