Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 40 Maths Textbook Solution.
Answer: The factory makes 4 tennis racket and 12 cricket bats. Maximum profit is 200.
Hint:
Let the number of tennis rackets and cricket bats be x and y.
Given:
A tennis racket takes 1.5 hours if machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman’s time. In a day factory has availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a rackets and bat is 20Rs and 10Rs.
Solution:
Let the number of tennis racket and cricket bats manufactured by factory be x and y.
Hence, Profit is the objective function Z.
Z = 20x + 10y … (i)
We have to maximize Z subject to the constraints.
… (ii) [Constraints for machine hour]
… (iii) [Constraints for craftman’s hour]
Graph of x = 0 and y = 0 is the y-axis and x-axis.
Graph of is the 1st quadrant.
Graph of
x |
0 |
28 |
y |
14 |
0 |
Graph for is the part of 1st quadrant which contains the origin.
Graph for
x |
0 |
8 |
y |
24 |
0 |
Graph for is the part of st quadrant in which origin lies.
Hence, shaded area OACB is the feasible region for coordinate of C equation
… (iv)
… (v)
X = 4 (Substituting y = 12 in (iv))
Now the value of objective function Z at each corner of feasible region is
Corner Points |
|
O(0,0) |
|
A(8,0) |
|
B(0,14) |
|
C(4,12) |
Therefore, maximum profit is Rs.200 when factory makes 4 tennis rackets and 12 cricket bats.