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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 35

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 35

Answers (1)

Answer: 48 units of product A and 16 units of product. Maximum profit = Rs.1440.

Hint:

Let x be the number of units A and y be the number of units of B

Given:

The given data can be written in the tabular form

 

 

Product

A

B

Working week

Turn over

Time

0.5

1

40

 

Price

200

300

 

10000

Profit

20

30

 

 

Permanent order

14

16

 

 

 

Solution:

The mathematical model of the LPP as follows.

Max Z = 20x + 30y

Subject to:

       \begin{aligned} &0.5 x+y \leq 40 \\ &200 x+300 y \geq 10000 \\ &x \geq 14, y \geq 16 \end{aligned}

Subject to constraint:

      \begin{aligned} &4 x+3 y \geq 60 \\ & \end{aligned}                                                … (i)

      x \geq 3 \\                                                                … (ii)

      y \geq 2 x \\                                                             … (iii)

      x, y \geq 0

The feasible region determined by the subject of constraints.

No of large box=6, small box=12

Maximum profit=Rs.42

The coordinates of the vertices (corner points) of shaded region ABCD are A(26,16),B(48,16),C(14,33) and D(14,24)                                        

Points

Z=20x+30y

A(26,16)

Z=1000

B(48,16)

Z=1440

C(14,33)

Z=1270

D(14,24)

Z=60

 

48 units of Product A and 16 units of Product B should be produced to earn the maximum profit of Rs.1440.

 

Posted by

infoexpert27

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