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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 52

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 52

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Answer: The maximum total revenue is Rs.1260 when 3 units of A and 8 units of B are produced. Yes, because the efficiency of a worker does not depend on whether the worker is a male or female.

Hint:

 Use property of LPP

Given:

 That men and women workers are equally efficient and So, he pays them at the same rate.

Solution:

Let x unit of A and y units of B produced by the manufacturer.

The price of one unit of A is Rs.100 and the price of one unit of B is Rs.120. Therefore, the total price of x unit of A and y units of B. The total revenue is Rs. (100x+120y) one unit of A requires 2 workers are one unit of B requires 3 workers. Therefore x unit of A and y units of B requires (2x + 3y) workers. But, the manufacturer has 30 workers.

                                                                2 x+3 y \leq 30

Similarly, one unit of A requires 3 units of capital. Therefore, x unit of A and y unit of B requires (3x+y) units of capital. Therefore, x unit of A and y unit of B requires (3x + y) units of capital. But the manufacturer has 17 units of capital.

                                                                \begin{aligned} &2 x+3 y \leq 30 \\ &3 x+y \leq 17 \\ &x, y \geq 0 \end{aligned}

The feasible region determined by the given constraints can be diagrammatically represented as.

The coordinates of the corner points of the feasible region are O(0,0), A(0,10), B(17/3,0) and C(3,8)

The value of the objective function at these points is given in the following table.

 

Corner Points

z=100x+120y

O

100 \times 0+120 \times 0=0

A

100 \times 0+120 \times 10=1200

B

100 \times \frac{17}{3}+120 \times 0=\frac{1700}{3}

C

100 \times 3+120 \times 8=1260 (maximum)

The maximum value of Z is 1260 at x=3 and y=8.

Hence the maximum total revenue is Rs.1260 when 3 units of A and 8 units of B are produced.

Yes, because the efficiency of a worker does not depend on whether the worker is a male or female.

Posted by

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