Currently, cable rate = 19 and subscribers = 900. 
For each 0.25 reduction in rate, subscribers will increase by 50.

Let us say the rate is reduced x times (each reduction = 0.25)
So the reduced rate = 19 - 0.25*x
For each reduction, subscribers go up by 50
So the new number of subscribers = 900 + 50*x

New revenue = 

For the revenue to be maximum, the first derivative of the expression has to 
be 0, and the second derivative has to be negative.

Revenue = 

First derivative = 

Solving for -25*x + 725 = 0, 

Second derivative = -25 which is negative, confirming that it is a max value.

So, the cable rate for maximum revenue = 
At this rate, number of customers = 

Max revenue will be 

Hope you got it. 

:)