An internet service provider in a town has 500 subscribers and charging ₹300 per month from each subscriber. He proposes to increase the monthly charges and it is believed from past experience that for every increase of ₹1, one subscriber will discontinue the service.

The number of subscribers for which the maximum revenue is earned is

400

Consider that company increases the annual subscription by $Rsx$
So $x$ subscribes will discontinue the service .
$\therefore$ Total revenue of company after the increment is given by 

$R(x)=(500-x)(300+x)$
=15×10⁴+500x−300x−x²

Revenue R(x) = -x² + 200x + 150000

Differentiating

R'(x) = -2x + 200, put R'(x) = 0

⇒ -2x + 200 = 0 ⇒ x = 100

R″(x) = -2 < 0 R(x) is maximum at x = 100

Number of subscriber for maximum revenue is 500 - 100 = 400.