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?

No feasible region exists.

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.