Which of the following is a corner point of the feasible region determined by the constraints \(x + 2y \ge 6\), \(2x + y \ge 6\), \(x \ge 0\), \(y \ge 0\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (2, 2)
Both constraints are of the “≥” type, so the region lies away from the origin and is unbounded.
The line 2x + y = 6 meets the y-axis at (0, 6), and the line x + 2y = 6 meets the x-axis at (6, 0). The two lines meet where
\(y = 6 - 2x\)
\(x + 2(6 - 2x) = 6\)
\(12 - 3x = 6\)
\(x = 2,\ y = 2\)
So the corner points are (0, 6), (2, 2) and (6, 0), and (2, 2) is one of them.
Why the other options are incorrect
Option (1) (0, 3) — Incorrect. There 2x + y = 3 < 6, so the point is not even feasible.
Option (2) (3, 3) — Incorrect. It is feasible (x + 2y = 9, 2x + y = 9), but it lies on no boundary line, so it is inside the region, not a corner.
Option (3) (3, 0) — Incorrect. There x + 2y = 3 < 6, so the point is not feasible.