The number of corner points of the feasible region determined by the constraints \(x + 2y \le 14\), \(3x + y \le 12\), \(x + y \ge 3\), \(x \ge 0\), \(y \ge 0\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
The region lies below both lines x + 2y = 14 and 3x + y = 12, and on the far side of x + y = 3 from the origin.
On the x-axis the region runs from (3, 0), on x + y = 3, to (4, 0), on 3x + y = 12.
On the y-axis it runs from (0, 3), on x + y = 3, to (0, 7), on x + 2y = 14.
The lines x + 2y = 14 and 3x + y = 12 meet where
\(y = 12 - 3x\)
\(x + 2(12 - 3x) = 14\)
\(x = 2,\ y = 6\)
Here x + y = 8 ≥ 3, so (2, 6) is feasible. The corner points are (3, 0), (4, 0), (2, 6), (0, 7) and (0, 3), that is, 5 corner points.