Which of the following points does NOT lie in the feasible region determined by the constraints \(2x + 3y \le 12\), \(x + y \le 5\), \(x \ge 0\), \(y \ge 0\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (2, 3)
A point is feasible only if it satisfies every constraint. All four points have \(x, y \ge 0\), so only the first two constraints need checking.
(3, 2): \(2x + 3y = 12 \le 12\), \(x + y = 5 \le 5\)
(4, 1): \(2x + 3y = 11 \le 12\), \(x + y = 5 \le 5\)
(0, 4): \(2x + 3y = 12 \le 12\), \(x + y = 4 \le 5\)
(2, 3): \(2x + 3y = 13 \gt 12\)
The point (2, 3) breaks \(2x + 3y \le 12\), so it is not in the feasible region. Points lying on a boundary line, such as (3, 2) and (0, 4), are still feasible.