Q9 of 97 Page 1376

A man has ₹1500 to purchase rice and wheat. A bag of rice and a bag of wheat cost ₹180 and 120 respectively. He has storage capacity of 10 bags only. He earns a profit of ₹11 and ₹8 per bag of rice and wheat respectively. How many bags of each must he buy to make maximum profit?


Let the number of wheat and rice bags be x and y.


∴According to the question,


120x + 180y, x + y,x


Maximize Z = 8x + 11y


The feasible region determined by 120x + 180y, x + y,xis given by



The corner points of feasible region are A(0,8), B(0,0), C(10,0), D(5,5) .


The value of Z at corner point is



The maximum value of Z is 95 at point (5,5).


Hence, the man should 5 bags each of wheat and rice to earn maximum profit.


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