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.
Rate this question :
A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of the first machine is 12 hours and that of the second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines, and each unit of product B requires 2 hours on the first machine and 1 hour on the second machine. Each unit of product A is sold at ` 7 profit and that of B at a profit of ` 4. Find the production level per day for maximum profit graphically.Mathematics - Board Papers
A retired person wants to invest an amount of ₹ 50,000. His broker recommends investing in two types of bonds ‘A’ and ‘B’ yielding 10% and 9% return respectively on the invested amount. He decides to invest at least ₹ 20,000 in bond ‘A’ and at least ₹ 10,000 in bond ‘B’. He also wants to invest at least as much in bond ‘A’ as in bond ‘B’. Solve this linear programming problem graphically to maximize his returns.Mathematics - Board Papers
A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs80 on each piece of type A, and Rs120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?Mathematics - Board Papers