Items are based on the information below:
A cable network provider in a small town has 500 subscribers and he used to collect Rs. 300 per month from each subscriber. He proposes to increase the monthly charges and it is believed from the past experience that for every increase of Rs. 1, one subscriber will discontinue the service. Based on the above information, answer the following question :
What is increase in charges per subscriber that yields maximum revenue?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 100
With an increase of Rs x, the revenue is
\(R = (300 + x)(500 - x)\)
\(= 150000 + 200x - x^2\)
For the maximum, set the derivative to zero:
\( \displaystyle \frac{dR}{dx} = 200 - 2x = 0 \Rightarrow x = 100 \)
\( \displaystyle \frac{d^2R}{dx^2} = -2 \lt 0 \)
So the revenue is maximum when the charge per subscriber is increased by Rs 100.
NCERT Exemplar:
Application of Derivatives
