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 increase in charges per subscriber per month that yields maximum revenue is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 100
With an increase of Rs. x, the charge is Rs. (300 + x) and 500 − x subscribers remain:
\(R(x) = (300 + x)(500 - x)\)
\(R(x) = 150000 + 200x - x^2\)
For a maximum, R’(x) = 0:
\(R'(x) = 200 - 2x = 0\)
\(x = 100\)
R’’(x) = −2 < 0, so this is a maximum. The increase is Rs. 100.
NCERT Exemplar:
Application of Derivatives
