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

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

Answers (1)

Answer:

The answer of the given question B that the firm should produce 8A products and 16B products to earn maximum profit of Rs.4960

Hint:

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

Given:

A small firm manufactures item A and B- The total number of items that it can manufacture in a day B at most 24. Item A takes one hour while items B takes only half an hour.

Solution:

Let the firm manufactures x members of A and y members of B products.

According to the question

                                    x+y \leq 24, x+0.5 y \leq 16, x \geq 0, y \geq 0

Maximize Z = 300x + 160y

The feasible region determined by  x+y \leq 24, x+0.5 y \leq 16, x \geq 0, y \geq 0   given by

The corner points of feasible region are A(0,0), B(0,24), C(8,16) and D(16,0)

The value of Z at corner point is

Corner Points

Z=300x+160y

 

A(0,0)

0

 

B(0,24)

3840

 

C(8,16)

4960

Maximum

D(16,0)

4800

 

The maximum value of Z is 4960 and occurs at point (8,16)

The firm should produce 8A products and 16 B products to earn maximum profit of Rs.4960.

 

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