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?
Answer & explanation
Correct answer: option 2
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