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7. A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?

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Let x be Souvenirs of type A and y be Souvenirs of type B .Thus, $x\geq 0,y\geq 0$ .

The given information can be represented in table as :

	Type A	Type B	availability
cutting	5	8	$(3\times 60)+20=200$
asembling	10	8	$4\times 60=240$

Profit on type A Souvenirs is Rs. 5 and on type B Souvenirs is 6.

Therefore, constraint are

$5x+8y\leq 200$

$10x+8y\leq 240$

$x\geq 0,y\geq 0$

$Z=5x+6y$

The feasible region determined by constraints is as follows:

The corner points of feasible region are $A(24,0),B(8,20),C(0,25),D(0,0)$

The value of Z at corner points is as shown :

Corner points	$Z=5x+6y$
$A(24,0)$	120
$B(8,20)$	160	maximum
$C(0,25)$	150
$D(0,0)$	0

The maximum value of z is 160 at $B(8,20)$ .

Thus,8 Souvenirs of type A and 20 Souvenirs of type B should be manufactured everyday to get maximum profit.

Posted by

seema garhwal

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