An internet service provider in a town has 500 subscribers and charging Rs. 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 Rs. 1, one subscriber will discontinue the service.
The maximum revenue generated per month is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 160000
Let the monthly charge be increased by Rs. x. Then the charge is Rs. (300 + x) and the number of subscribers is 500 − x, so the revenue is
\(R(x) = (300 + x)(500 - x)\)
\(R(x) = 150000 + 200x - x^2\)
For a maximum, R’(x) = 0:
\(R'(x) = 200 - 2x = 0\)
\(x = 100\)
R’’(x) = −2 < 0, so R is maximum at x = 100:
\(R(100) = 400 \times 400 = 160000\)
The maximum monthly revenue is Rs. 160000.