Consider the Linear Programming Problem
Maximize $z = x+y$
Subject to the constraints $x-y≤ -1, x≥y, x≥0,y≥0$
Then which one of the following is TRUE?

There is no solution

The correct answer is Option (2) → There is no solution

Given LPP:

Maximize $z = x + y$

Subject to constraints:

$x - y \leq -1$

$x \geq y$

$x \geq 0$

$y \geq 0$

Analyze constraints:

From $x - y \leq -1$, rearranged:

$x \leq y - 1$

From $x \geq y$, also $x \geq y$

So:

$x \leq y - 1$ and $x \geq y$ simultaneously

This implies:

$y \leq x \leq y - 1$

Which is impossible, since $y - 1 < y$ always.

Also, $x, y \geq 0$.

Therefore, no $x,y$ satisfy the constraints simultaneously.

Answer: There is no solution