Question

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?

Answer 1

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

∴According to the question, 

20x + 25y ≤ 1400, 10x + 20y ≤ 1000, x ≥ 0, y ≥ 0

Maximize Z = 40x + 60y 

The feasible region determined by 20x + 25y ≤ 1400, 10x + 20y ≤ 1000, x ≥ 0, y ≥ 0 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

Corner Point	Z = 40x + 60y
A(0, 0)	0
B(0, 50)	3000
C(20, 40)	3200	Maximum
D(70, 0)	2800

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