Q16 of 97 Page 1376

A toy company manufactures two types of dolls, A and B. Each doll of type B take twice as long to produce as one of type A, and the company would have time to make a maximum of 2000 per day, if it produces only type A. the supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined ). Type B requires a fancy dress of which there are only 600 per day available. If the company makes profit of ₹3 and ₹5 per dolls respectively on dolls A and B, how many of each should be produced per day in order to maximize the profit? Also, find the maximum profit.


Let x and y be number of doll A manufactured and doll B manufactured.


∴According to the question,


x + y 1500, x + 2y y


Maximize Z = 3x + 5y


The feasible region determined by x + y 1500, x + 2y yis given by



The corner points of feasible region are A(0,0) , B(0,600) , C(800,600),D(1000,500),E(1500,0).


The value of Z at corner points are



The maximum value of Z is 5500 at point (1000,500).


Hence, the manufacturer should produce 1000 types of doll A and 500 types of doll B to make maximum profit of Rs.5500.


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A manufacture of a line of patent medicines is preparing a production plan on medicines A and B. There are sufficient ingredients available to make 20000 bottles of A and 40000 bottles of B but there are only 45000 bottles into which either of the medicines can be put. Furthermore, it takes 3 hours to prepare enough material to fill 1000 bottles of A and it takes 1 hour to prepare enough material to fill 1000 bottles of B, and there are 66 hours available for this operation. The profit is ₹8 per bottle for A and ₹7 per bottle for B.

How should the manufacture schedule the production in order to maximize his profit? Also, find the maximum profit.


 15

A manufacture of a line of patent medicines is preparing a production plan on medicines A and B. There are sufficient ingredients available to make 20000 bottles of A and 40000 bottles of B but there are only 45000 bottles into which either of the medicines can be put. Furthermore, it takes 3 hours to prepare enough material to fill 1000 bottles of A and it takes 1 hour to prepare enough material to fill 1000 bottles of B, and there are 66 hours available for this operation. The profit is ₹8 per bottle for A and ₹7 per bottle for B.

How should the manufacture schedule the production in order to maximize his profit? Also, find the maximum profit.


 16

A toy company manufactures two types of dolls, A and B. Each doll of type B take twice as long to produce as one of type A, and the company would have time to make a maximum of 2000 per day, if it produces only type A. the supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined ). Type B requires a fancy dress of which there are only 600 per day available. If the company makes profit of ₹3 and ₹5 per dolls respectively on dolls A and B, how many of each should be produced per day in order to maximize the profit? Also, find the maximum profit.

 17

A small manufacture has employed 5 skilled men and 10 semiskilled men and makes an article in two qualities, a deluxe model and an ordinary model. The making of a deluxe model requires 2hours work by a skilled man and 2hours work by a semiskilled man. The ordinary model requires 1 hour by a skilled man and 3 hours by a semiskilled man. By union rules, no man can work more than 8 hours per day. The manufacture gains ₹15 on the deluxe model and ₹10 on the ordinary model. How many of each type should be made in order to maximize his total daily profit? Also, find the maximum daily profit.