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  • A merchant plans to sell two types of personal computers .Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs

8. A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

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Let  merchant plans has  personal computers  x  desktop 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.

  25000x+40000y\leq 7000000

  5x+8y\leq 1400

the total monthly demand of computers will not exceed 250 units.

  x+y\leq 250

profit on the desktop model  is Rs 4500 and on portable model is Rs 5000.

Total profit = Z , Z=4500x+5000y

The mathematical formulation of given problem is :
 5x+8y\leq 1400

 x+y\leq 250

 x\geq 0,y\geq 0

 Z=4500x+5000y

The feasible  region determined by constraints is as follows:

    

The corner points of feasible region are  A(250,0),B(200,50),C(0,175),D(0,0)

The value of Z at corner points is as shown :

Corner points

Z=4500x+5000y

  
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

seema garhwal

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