For the LPP Max $Z= 3x+4y , x+ y ≤40;

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Linear Programming

Question:

For the LPP Max $Z= 3x+4y , x+ y ≤40; x+2y ≤60, x ≥0, y ≥ 0$ the solution is :

Options:

$x=20, y = 20,$ Max $Z=140$

$x=40, y = 0,$ Max $Z=120$

$x=0, y = 60,$ Max $Z=240$

$x=10, y = 30,$ Max $Z=130$

Correct Answer:

$x=20, y = 20,$ Max $Z=140$

Explanation:

The correct answer is Option (1) → $x=20, y = 20,$ Max $Z=140$

$Z= 3x+4y$

and,

$x+ y ≤40$

$x+2y ≤60$

$x, y ≥ 0$

∴ $Z_{max}$ at (20, 20)

$⇒Z=3×20+4×20=140$