Q. 22

# A man owns a field area 1000 m2. He wants to plant fruit trees in it. He has a sum of ₹1400 to purchase young trees. He has the choice of two types of trees. Type A requires 10 m2 of ground per trees and costs ₹20 per tree, and type B requires 20 m2 of ground per tree and costs ₹25 per tree. When full grown, a type - A tree produces an average of 20 kg of fruit which can be sold at a profit ₹2 per kg and type - B tree produces an average of 40 kg of fruit which can be sold at a profit of ₹1.50 per kg. How many of each type should be planted to achieve maximum profit when tree are full grown? What is the maximum profit?

Let x and y be number of A and B trees.

According to the question,

20x + 25y , 10x + 20y

Maximize Z = 40x + 60y

The feasible region determined by 20x + 25y , 10x + 20y is given by

The corner points of feasible region are A(0,0) , B(0,50) , C(20,40), D(70,0).The value of Z at corner points are

The maximum value of Z is 3200 at point (20,40).

Hence, the man should plant 20 A trees and 40 B trees to make maximum profit of Rs.3200.

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