Which of the following is NOT a corner point of the feasible region determined by the constraints \(x + y \le 6\), \(x - y \le 2\), \(x \ge 0\), \(y \ge 0\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \((3, 3)\)
A corner point is a point of the region where two boundary lines meet. The corner points here are:
(0, 0), where \(x = 0\) meets \(y = 0\)
(2, 0), where \(x - y = 2\) meets \(y = 0\)
(0, 6), where \(x + y = 6\) meets \(x = 0\)
The fourth one is where \(x + y = 6\) meets \(x - y = 2\):
\(2x = 8\)
\(x = 4, \; y = 2\)
The point (3, 3) is feasible, but it lies only on the line \(x + y = 6\), between (4, 2) and (0, 6). It is a point of an edge, not a corner point.