Which of the following points lies in the feasible region determined by the constraints \(x + 2y \le 8\), \(3x + y \le 9\), \(x \ge 0\), \(y \ge 0\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \((2, 3)\)
A point is in the feasible region only if it satisfies every constraint. For (2, 3):
\(x + 2y = 2 + 6 = 8 \le 8\)
\(3x + y = 6 + 3 = 9 \le 9\)
Both hold (the point lies on both boundary lines), and \(x, y \ge 0\), so (2, 3) is feasible.
Why the other options are incorrect
Option (1) \((3, 1)\) — Incorrect. \(3x + y = 10 \gt 9\).
Option (2) \((1, 4)\) — Incorrect. \(x + 2y = 9 \gt 8\).
Option (3) \((4, 0)\) — Incorrect. \(3x + y = 12 \gt 9\).