Q. 93.5( 2 Votes )

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?

Answer :

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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