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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 53

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 53

Answers (1)

Answer: The maximum daily profit of the manufacturer is Rs.26

Hint:

 Use property of LPP

Given:

First machine is 12 hours and second machine is 9 hours per day.

Solution:

Let x units of product A and y units of Product B be manufactured by the manufacturer per dat.

It is given that one unit of product A requires 3 hours of processing time on first machine, while one unit of product B requires 2 hours of processing time on first machine.

It is also given that first machine is available for 12 hours per day.

                3 x+2 y \leq 12

Also, one unit of product A requires 3 hours of processing time on second machine, while one unit of product B requires 1 hour of processing time on second machine.

It is also given that second machine is available for 9 hours per day.

                3 x+y \leq 9

The profits on one unit each of Product A and B are Rs.7 and Rs.4 respectively.

So the objective function is given by,

                Z=R s .(7 x+4 y)

Hence the mathematical formulation of the LPP is

Maximize Z=7x+4y

Subject to the constraints

                3 x+2 y \leq 12 \\                                       … (i)

                3 x+y \leq 9 \\                                            … (ii)

                \begin{aligned} & &x \geq 0, y \geq 0 \end{aligned}                                         … (iii)

The feasible region determined by constraints (1) and (2) is graphically represented as

Here it is seen that OABCO is the feasible region and it is bounded. The value of Z at the corner points of the feasible region are represented in tabular form as follows.

 

Corner Points

z=70x+4y

O(0,0)

7 \times 0+4 \times 0=0

A(3,0)

7 \times 3+4 \times 0=21

B(2,3)

7 \times 2+4 \times 3=26 (maximum)

C(0,6)

7 \times 0+4 \times 6=24

The maximum value of Z is 26, which is obtained at x = 2 and y = 3.

Thus, 2 units of Product A and 3 units of product B. Should be manufactured by the manufacturer per day in order to maximize the profit.

Also, the maximum daily profit of the manufacturer is Rs.26.

Posted by

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