Consider the feasible region determined by the constraints \(x + y \ge 5\), \(x \le 4\), \(y \le 4\), \(x \ge 0\), \(y \ge 0\), and the following statements:
(A) The origin is an infeasible solution.
(B) The point \((3, 1)\) is a feasible solution.
(C) The feasible region is unbounded.
(D) The feasible region has exactly 3 corner points.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (D) only
The region lies above the line \(x + y = 5\) and inside the square \(0 \le x \le 4\), \(0 \le y \le 4\). The line \(x + y = 5\) meets the sides of the square at
\(x = 4\): \(y = 1\), point (4, 1)
\(y = 4\): \(x = 1\), point (1, 4)
So the feasible region is the triangle with corner points (1, 4), (4, 1) and (4, 4), and a point is feasible only if \(x + y \ge 5\) with \(x, y \le 4\).
Checking the statements
(A) The origin is an infeasible solution. — Correct. At (0, 0), \(x + y = 0 \lt 5\).
(B) The point \((3, 1)\) is a feasible solution. — Incorrect. At (3, 1), \(x + y = 4 \lt 5\).
(C) The feasible region is unbounded. — Incorrect. It is a triangle inside the square of side 4, so it is bounded.
(D) The feasible region has exactly 3 corner points. — Correct. The corners are (1, 4), (4, 1) and (4, 4).