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
Answer & explanation
Correct answer: option 4
Consider that company increases the annual subscription by Rs x
So x subscribes will discontinue the service .
∴ 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.