Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Linear Programming

Question:

A firm makes pants and shirt. A shirt takes 2 hour on machine and 3 hour of man labour while a pant takes 3 hour on machine and 2 hour of man labour. In a week there are 70 hour of machine and 75 hour of man labour available. If the firm determines to make x shirts and y pants per week, then for this the linear constraints are

Options:

$x \geq 0, y \geq 0,2 x+3 y \geq 70,3 x+2 y \geq 75$

$x \geq 0, y \geq 0,2 x+3 y \leq 70,3 x+2 y \geq 75$

$x \geq 0, y \geq 0,2 x+3 y \geq 70,3 x+2 y+\leq 75$

$x \geq 0, y \geq 0,2 x+3 y \leq 70,3 x+2 y \leq 75$

Correct Answer:

$x \geq 0, y \geq 0,2 x+3 y \leq 70,3 x+2 y \leq 75$

Explanation:

 

 Working time on machine 

 Man labour 

 Shirt (x)

2 hours

3 hours

 Pant (y)

3 hours

2 hours

 Availability 

70 hours

75 hours


Linear constraints are $2 x+3 y \leq 70,3 x+2 y \leq 75$ and $x, y \geq 0$