Question

A cable network provider in a small town has 500 subscriber and he used to collect Rs. 300 per month from each subscriber. He proposes o 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 the increase in the changes per subscriber that yields maximum revenue?

• A. 100
• B. 200
• C. 300
• D. 400

Answer 1

The Correct Option is A

Let company increases the annual subscription by \(Rs\ x\).
So, x subscribers will discontinue the service.
Total revenue of company after the increment
\(R(x) =(500−x)(300+x)\)
\(R(x) =1500000+500x−300x−x^2\)
\(R(x) = −x^2+200x+150000\)
Differentiate both sides w.r.t, x
\(R^′(x)=−2x+200\)
Now, \(R^′(x)=0\)
\(2x=200\)
\(x=100\)
∴ \(R^{''}(x)=−2<0\)
R(x) is maximum when \(x = 100\).
Therefore, the company should increase the subscription fee by \(Rs.\ 100\), so that it has maximum revenue.
So, the correct option is (A): \(100\)