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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.

 

 

 

 

 

 

 

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