Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Linear Programming

Question:

The feasible region of an LPP Max $Z=3x+2y$ subject to $x ≥0, y≥0, x-2y≤3$ is:

Options:

Bounded in first quadrant but has no solution

Unbounded in first quadrant but has a solution

Unbounded in first quadrant and has no solution

Bounded and has a solution $x = 0, y = 0, Z=0$

Correct Answer:

Unbounded in first quadrant and has no solution

Explanation:

$Z=3x+2y$

$x ≥0, y≥0$ → solution in first quadrant plotting $x-2y=3$ first

  x     3   0
y 0 -3/2

now checking for (0, 0)

$x - 2y ≤3$

$⇒0≤3$

So solution has two side of $x-2y=3$ containing (0, 0)