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.



Let x and y be number of bottles of medicines A and B be prepared.


∴According to the question,


x + y 45000 , 3x + y 66000, x , y,


Maximize Z = 8x + 7y


The feasible region determined by x + y 45000 , 3x + y 66000, x , y, is given by



The corner points of feasible region are A(0,0) , B(0,40000) , C(5000,40000),D(10500,34500),E(20000,6000),F(20000,0).


The value of Z at corner points are



The maximum value of Z is 325500 at point (10500,34500).


Hence, the manufacturer should produce 10500 bottles of medicine A and 34500 bottles of medicine B.


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