Aspire Faculty ID #17282 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

A cable network provider in a small town has $500$ subscribers and he used to collect Rs. $300$ per month from each subscriber. He proposes to increase the monthly charges and it is believed that for every increase of Rs. $1$, one subscriber will discontinue the service. The maximum revenue generated is:

Solution

Revenue function:

$R=(300+x)(500-x)$

Expand:

$R=150000+200x-x^2$

This quadratic is maximum at

$x=100$

Now substitute:

$R=(300+100)(500-100)$

$R=400\times 400$

$R=160000$

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