Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Linear Programming

Question:

The feasible region for an LPP is shown in the given figure.

Constraints for the LPP are :

Options:

$2x+y≤50, x+2y ≤ 40, x ≥ 0, y ≥ 0$

$2x+y≥50, x+2y ≥ 40, x≥ 0, y ≥ 0$

$2x+y≤50, x+2y ≥ 40, x≥ 0, y ≥ 0$

$2x+y≥50, x+2y ≤ 40, x≥ 0, y ≥ 0$

Correct Answer:

$2x+y≤50, x+2y ≤ 40, x ≥ 0, y ≥ 0$

Explanation:

From the given graph, the shaded feasible region is bounded by the coordinate axes and two straight lines.

The corner points visible are:

O(0,0), C(0,20), B(20,10), A(25,0)

Equation of line CB through (0,20) and (20,10):

$\frac{y-20}{10-20}=\frac{x-0}{20-0}$

$y= -\frac{1}{2}x+20$

Equation of line BA through (20,10) and (25,0):

$\frac{y-10}{0-10}=\frac{x-20}{25-20}$

$y=-2x+50$

Hence the constraints of the LPP are:

$x \ge 0$

$y \ge 0$

$y \le -\frac{1}{2}x+20$

$y \ge -2x+50$ is NOT included since region lies below this line

$x \le 25$ (from point A)

final answer: The constraints are $x\ge0,\; y\ge0,\; y\le -\frac{1}{2}x+20,\; y\le -2x+50,\; x\le25$