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A merchant plans to sell two types of...

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 nu

Text Solution

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Let number of desktops be `x`,
and number of portable computers be `y`



According to Question:
Monthly demand of both items = maximum 250 units
`therefore x+y<=250 " " " " ....(1)`

Also,
Cost of Desktop = Rs 25000
Cost of Computers= Rs 40000
Max Investment = Rs 70,00,000

Hence,
` " " " 25000x+40000y<=70,00,000`
` " " " 5x+8y<=1400 " " " " ....(2)`

As we need to maximize profit,
Hence, Function used here will be Maximize `Z`

Profit on Desktop `to` Rs 4500
Profit on Computers `to` Rs 5000
`therefore` Maximize `Z=4500x+5000y`

Combining all constraints
Max `Z=4500x+5000y`
`x+y<=250`
`5x+8y<=1400`
`x>=0, y>=0`







Hence, the profit will be maximum if company produces:
Number of desktops =200
Number of portable computers = 50

Maximum Profit = Rs 11,50,000
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