A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs 300 per subscriber. The company proposes to increase the annual subscription and it is believed that every increase of Rs 1 one subscriber will discontinue the service. Find what increase will bring maximum revenue?

Explanation

Consider that company increases the annual subscription by Rs x.
So, x subscribers will discontinue the service.
`therefore` Total revenue of company after the increment is given by
R(x) `= (500-x)(300+x)`
`=15 xx 10^(4) + 500x- 300x-x^(2)`
`=-x^(2)+200x+150000`
On differentiating both sides w.r.t, x, we get
`R^(')(x)=-2x+200`
Now, `R^(')(x)=0`
`rArr 2x=200 rArr x=100`
`therefore R^('')(x)= -2 lt0`
So, R(x) is maximum when x=100.
Hence, the company should increase the subscription fee by Rs 100, so that it has maximum profit.