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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PREVIOUSA 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?NEXTA manufacture produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine A and 3 hours on machine B to produces a packet of nuts while it takes 3 hours on machine A and 1 hours on machine B to produce a packet of bolts. He earns a profit ₹17.50 per packet on nuts and ₹7 per packet on bolts. How many packets of each should be produced each day so as to maximize his profit if he operates each machine for at the most 12 hours a day? Also find the maximum profit.

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