A company manufactures two types of screws A | vedclass

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Question

Let the company manufactures $x$ boxes of type $A$ screws and $y$ boxes of type $B$ screws.

From the given information, we have following correspon

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Let the company manufactures $x$ boxes of type $A$ screws and $y$ boxes of type $B$ screws.

From the given information, we have following corresponding constraint table.


	
		
			 
			Type $A \,(x)$
			Type $B \,(y)$
			Maximum time available on each machine in a week
		
		
			Time required for screws on threading machine
			$2$
			$8$
			$60 	imes 60(\min )$
		
		
			
			Time required for screws on slotting machine
			
			$3$
			$2$
			$60 	imes 60(\min )$
		
		
			Profit
			$Rs.\,100$
			$Rs.\,170$
			 
		
	


Thus, the objective function for maximum profit is $Z=100 x+170 y$ Subject to constraints

$2 x+8 y \leq 60 	imes 60$ [time constraint for threading machine]

$\Rightarrow \quad x+4 y \leq 1800$

and $3 x+2 y \leq 60 	imes 60$ [time constraint for slotting machine]

$\Rightarrow \quad 3 x+2 y \leq 3600$

Also, $x \geq 0, y \geq 0$ [non-negative constraints]

$	herefore$ Required $LLP$ is,

Maximize $Z=100 x+170 y,$ subject to constraints

$x+4 y \leq 1800,3 x+2 y \leq 3600, x \geq 0, y \geq 0$

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	Type $A \,(x)$	Type $B \,(y)$	Maximum time available on each machine in a week
Time required for screws on threading machine	$2$	$8$	$60 \times 60(\min )$
Time required for screws on slotting machine	$3$	$2$	$60 \times 60(\min )$
Profit	$Rs.\,100$	$Rs.\,170$