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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 45

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 45

Answers (1)

Answer: The merchant should stock 200 desktop models and 50 portable models to get maximum profit.

Hint:

Let merchant plans has personal computers x desktop model and y portable model.

Given:

Cost of desktop model computer=25000

Cost of portable model computer=40000

Total monthly demand will not exceed 250 units.

Profit on desktop model=4500Rs.

Profit on portable model=5000Rs.

Solution:

Let merchant plans has personal computers x desktops model and y portable model.

Thus, x \geq 0 \& y \geq 0

The cost of desktop model is cost Rs.25000 and portable model is Rs.40000

 Merchant can invest Rs.70 lakhs maximum

      \begin{aligned} &25000 x+40000 y \leq 700000 \\ &5 x+8 y \leq 1400 \end{aligned}

The total monthly demand will not exceed 250 units.

        x+y \leq 250

Profit on desktop model is 4500 and on portable model is Rs.5000

Total Profit = Z,

        Z=4500 x+5000 y                                                             

The feasible region determined by constraints is as follows.

                                                                        

                                                                    

The corner points of feasible region are A(25,0), B(250,50), C(0,175) , D(0,0)

The value of Z corner points is as shown

 

Corner Points

Z=4500x+500y

A(250,0)

1125000

B(200,50)

1150000(Maximum)

C(0,175)

875000

D(0,0)

0

 

 The maximum value of Z is 1150000 at B(200,50)

Thus, merchant should stock 200 desktop models and 50 portable models to get maximum profit.

 

 

 

 

 

 

 

Posted by

infoexpert27

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