Q21 of 97 Page 1376

A manufacture makes two product, A and B. product A sells at ₹200 each and takes hour to make. Product B sells at ₹300 each and takes 1 hour to make. There is a permanent order for 14 of product A and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than ₹10000. If the profit on each of the product A is ₹20 and on product B, it is ₹30 then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.


Let x and y be number of A and B products.


∴According to the question,


0.5x + y , 200x + 300y


Maximize Z = 20x + 30y


The feasible region determined by 0.5x + y , 200x + 300y is given by



The corner points of feasible region are A(14,33) , B(14,24) , C(26,16), D(48,16).The value of Z at corner points are



The maximum value of Z is 1440 at point (48,16).


Hence, the manufacturer should manufacture 48 A products and 16 B products to maximize their profit of Rs.1440.


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A manufacture makes two types, A and B, of teapots. Three machines are needed for the manufacture and the time required for each teapot on the machines is given below.

Each machine is available for a maximum of 6 hours per day. If the profit on each teapot of type A is 75 paise and that on each teapot of type B is 50 paise, show that 15 teapots of type A and 30 of type B should be manufactured in a day to get the maximum profit.



 21

A manufacture makes two product, A and B. product A sells at ₹200 each and takes hour to make. Product B sells at ₹300 each and takes 1 hour to make. There is a permanent order for 14 of product A and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than ₹10000. If the profit on each of the product A is ₹20 and on product B, it is ₹30 then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.

 22

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