The number of corner points of the feasible region determined by the constraints \(2x + y \le 12\), \(x + y \ge 3\), \(x \ge 0\), \(y \ge 0\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
The line \(2x + y = 12\) meets the axes at (6, 0) and (0, 12). The line \(x + y = 3\) meets the axes at (3, 0) and (0, 3).
The two lines meet where
\(2x + y - (x + y) = 12 - 3\)
\(x = 9, \; y = -6\)
This point is not in the first quadrant, so the lines do not meet inside the region.
The feasible region lies below \(2x + y = 12\) and above \(x + y = 3\) in the first quadrant. It is the quadrilateral with corner points
(3, 0), (6, 0), (0, 12), (0, 3)
So there are 4 corner points.