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?

Answer :


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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Range of Quadratic/quadratic & linear/Linear functionsRange of Quadratic/quadratic & linear/Linear functionsRange of Quadratic/quadratic & linear/Linear functions45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :