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 maximum revenue generated is

Rs. 160000

The correct answer is Option (1) → Rs. 1,60,000

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,

$-2x+200=0$

$x=100$

∴ R'(x) Maximum = $1,50,000+200(100)-(100)^2$

$1,50,000+20,000-10,000$

$=1,60,000$