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  • Need solution for RD Sharma Maths Class 12 Chapter 29 Linear Programmig Excercise 29.4 Question 30

Need solution for RD Sharma Maths Class 12 Chapter 29 Linear Programmig Excercise 29.4 Question 30

Answers (1)

Answer:

The answer of the given question is that the maximum profit is Rs.1500 at E(12,15)

Hint:

By using the mathematical formulation of the given Linear programming is Max Z=ax + by

Given:

Two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling.

Solution:

 

Toy A

Toy B

Times in a day

Cutting time

5 min

8 min

180 min

Assembly time

10 min

8 min

240 min

Profit

50

60

 

Assumed Quantity

x

y

 

 

Profit function Z=50x+60y

\begin{aligned} &x \geq 0, y \geq 0 \\ &5 x+8 y \leq 180 \\ &10 x+8 y \leq 240 \text { or } 5 x+4 y \leq 120 \end{aligned}

                                               

         5 x+8 y=180                                                                          

 

A

B

x

0

36

y

22.5

8

         5 x+4 y \leq 120

 

C

D

x

0

24

y

30

0

 

Corner Points

z=50 x+60 y

At O(0,0)

0

At D(24,0)

1200

At E(12,15)

1500

At A(0,22.5)

1350

Hence the maximum profit is Rs.1500 at E(12,15)

Posted by

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