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

• A. $x \geq 0,y \geq 0,2x + 3y \geq 70,3x + 2y \geq 75$
• B. $x \geq 0,y \geq 0,2x + 3y \leq 70,3x + 2y \geq 75$
• C. $x \geq 0,y \geq 0,2x + 3y \geq 70,3x + 2y + \leq 75$
• D. $x \geq 0,y \geq 0,2x + 3y \leq 70,3x + 2y \leq 75$

Answer 1

Answer: (D)

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

Answer 2

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