For the linear programming problem (LPP), Maximize $Z = 7x+9y$, subject to constraints, $x-y≤-1,-x + y ≤0, x, y ≥ 0$. Which of the following is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → No feasible region exists.
Given LPP: Maximize $Z = 7x + 9y$
Subject to constraints:
$x - y \le -1 \Rightarrow y \ge x + 1$
$-x + y \le 0 \Rightarrow y \le x$
$x \ge 0, y \ge 0$
Check feasibility: For any point, $y \ge x + 1$ and $y \le x$ must hold simultaneously.
But $x + 1 \le y \le x$ is impossible for any $x$.
Hence, no feasible region exists.