Maths. Section B1Linear Programming

The feasible region corresponding to the linear constraints of a Line…

The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP?

$Graph of the shaded feasible region$

Answer & explanation

Correct answer: option 3

The correct answer is Option (3) → $x-y \ge 1$

Every point of the feasible region satisfies every constraint. The shaded region is bounded by the y-axis and the lines $x + 2y = 10$, $x + y = 2$ and $x - y = 1$. The point (1, 3) lies inside it. At (1, 3):

$x + 2y = 7$, so $x + 2y \le 10$ holds.

$x + y = 4$, so $x + y \ge 2$ holds.

$x - y = -2$, so $x - y \le 1$ holds and $x - y \ge 1$ fails.

So the region lies on the side $x - y \le 1$ of the line $x - y = 1$, and $x - y \ge 1$ is not a constraint of this LPP.