Provide Solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 25
Answer:
Maximum Profit Rs.1800 when Rs.20 were involved in Type A and Rs.40 were involved in Type B.
Hint:
Form Linear Equation and solve graphically.
Given:
A men owns a field of area 1000 m2. He wants to plant fruit trees in it. He has a sum of Rs.1400 to purchase young trees. He has the choice of two types of trees. Type A require 10 m2 of ground per tree and costs Rs.20 per tree and type B requires 20m2 of ground per tree and costs Rs.25 per tree. When fully grown type A produces an average of 20 kg of fruit which can be sold at a profit of Rs.2.00 per kg and type B produces an average of 40 kg of fruit which can be sold at a profit of Rs.1.50 per kg.
Solution:
Let the required number of trees of Type A and B be Rs.x and Rs.y respectively.
Number of trees cannot be negative.
To plant tree of Type A requires 10sq.m and Type B requires 20sq.m of ground per tree. And it is given that a man owns a field of are 1000sq.m.
Therefore,
Type A costs Rs.20 per tree and type B costs Rs.25 per tree. Therefore, x trees of type A and y trees of type B cost Rs.20x and Rs.25y respectively. A man has a sum of Rs.1400 to purchase young trrs
Thus the mathematical formulation of the given LPP is
Max Z = 40x -20x + 60y - 25y = 20x + 35y
Subject to,
Region : the line meets axes at A1(70,0) and B1(0,56)respectively.
The region which contains origin represents as (0,0) satisfies .
Region : the line meets axes at A2(70,0) and B2(0,56)respectively.
The region which contains origin represents as (0,0) satisfies .
Region : It represents by first quadrant.
The maximum value of Z is 1800 which is attained at P(20,40) as
The value of Z at these corner points are as follows
Corner Points |
|
O |
0 |
A1 |
1750 |
P |
1800 |
B2 |
1400 |
Thus the, max profit is Rs.1800 obtained when Rs.20 were involved in Type A and Rs.40 were involved in Type B.