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in Linear Programming by (91.4k points)
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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 `x` and `y` be the number of desktop and protable computers respectively.
According to the problem,
Maximum profit `Z=4500x+5000y`
and constraints `xge0, yge0`
`x+yle250`
`25000x+40000yle7000000`
`implies25x+40yle7000`
`implies25x+40y le7000`
First, draw the graph of the lines `x+y=250` and `25x+40y=7000`.
Now, find the feasible region from the constraints `xge0,yge0,x+yle250, 25x+40yle7000` and shade it. The vertices of this shaded region are `A(250,0),B(200,50)` and `C(0,175)`. We find the value of `Z` at these vertices.
image
For the the maximum profit 200 desktop and 50 portable computers should be produced.

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