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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 44

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 44

Answers (1)

Answer:

  1. 4 Tennis Racket Bats must be made so that factory runs at all capacity.
  2. Maximum profit is 200 when 4 tennis and 12 cricket balls are produced.

Hints:

Let the number of tennis racket be x number of cricket bat be y

Given:

 

Item

Number

Machine hours

Crafts man hours

Profit

Tennis Racket

x

1.5

3

Rs.20

Cricket Bats

y

3

1

Rs.10

Maximum time available

 

42

24

 

 

Solution:

Let the number of Tennis Racket be x.

Number of cricket bats be y.

According to the question,

 

 

 

              Machine hours                                                    Craftsman’s hours

                                    

            Tennis Racket – 1.5 hours                   Tennis Racket requires -3 hours

            Cricket bat requires – 3 hours              Cricket Bat requires – 1 hour

    Maximum time available – 42 hours        Max time available – 24 hour

\begin{aligned} &1.5 x+3 y \leq 42 \\ & \end{aligned}

 3 x+6 y \leq 84 \\                               3 x+y \leq 24

 x+2 y \leq 28                                 Also  x \geq 0, y \geq 0

As we want maximize the profit.

Hence function used here will be maximize

 profit on each tennis rocket  à Rs.20

Profit on each Bat                     à Rs.10

Max Z = 20x + 10y

Combining all the constraints:

Maximize Z = 20x + 10y

Subject to the constraints:

      \begin{aligned} &x+2 y \leq 28 \\ &3 x+y \leq 24 \\ &x \geq 0, y \geq 0 \end{aligned}

Now:

x+2 y \leq 28                                                        

 

x

0

14

 y

14

7

 

3 x+y \leq 24

 

x

2

8

 y

18

0

Corner Points

Value of Z

(0,4)

14

(4,12)

16

(8,0)

8

 

Thus,

  1. 4 Tennis Racket Bats must be made so that factory runs at all capacity.
  2. Maximum profit is 200 when 4 tennis and 2 cricket balls are produced.

 

Posted by

infoexpert27

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