Item 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 in formation, answer the following question :

The number of subscribers which gives the maximum revenue is

400

The correct answer is Option (4) → 400

Let x = increase in price per subscriber (in Rs.)

P(x) = New price per subscriber = 300 + x

N(x) = New number of subscribers = 500 - x

Revenue function, R(x) = Price per subscriber × Number of subscribers 

$R(x)=(300+x)(500-x)$

$=1,50,000+200x-x^2$

$∴R'(x)=-2x+200$

for critical point,

$-2x+200=0$

$x=100$

The number of subscribers is given by,

$N(x)=500-x$

$=500-100$

$=400$