The corner points of the feasible region determined by the constraints \(x + y \le 5\), \(x \le 3\), \(x \ge 0\), \(y \ge 0\) are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (0, 0), (3, 0), (3, 2) and (0, 5)
The region lies in the first quadrant, below the line x + y = 5 and to the left of the line x = 3.
The line x + y = 5 meets the y-axis at (0, 5). Its x-intercept (5, 0) breaks \(x \le 3\), so on the x-axis the region stops at (3, 0).
The lines x = 3 and x + y = 5 meet where
\(3 + y = 5\)
\(y = 2\)
So the corner points are (0, 0), (3, 0), (3, 2) and (0, 5).
Why the other options are incorrect
Option (1) (0, 0), (3, 0) and (0, 5) only — Incorrect. It leaves out (3, 2), where the line x = 3 meets x + y = 5.
Option (3) (0, 0), (5, 0), (3, 2) and (0, 5) — Incorrect. The point (5, 0) breaks \(x \le 3\).
Option (4) (0, 0), (3, 0), (3, 5) and (0, 5) — Incorrect. At (3, 5), x + y = 8 > 5, so it is not feasible.