Posted by Anonymous on Monday, May 25, 2009 at 10:47pm.
a cable television firm presently serves 5000 households and charges $20 per month. A merketing survey indicates that each decrease of $1 in the monthly charge will result in 500 new costumers. Let R(x)denote the total monthly revenue when the monthly charge is x dollars.
Determine the revenue function R

math  Reiny, Monday, May 25, 2009 at 11:10pm
let the number of $1 decreases be n
then the monthly cost = 20n
number of customers = 5000 + 500n
but you want 20n = x
so n = 20x
and 5000 + 500n
= 5000 + 500(20x)
= 5000 + 10000  500x
= 15000500x
so P(x) = x(15000  500x) or 15000  500x^2
(this is a very common question, but it is strangely worded.
Usually the question would be,
"What should be monthly charge for a maximum revenue ?" )

math  Anonymous, Monday, May 25, 2009 at 11:23pm
why do u multiply everything by x at the end? and what is 15000500x equal to? the number of costumers?

math  Reiny, Monday, May 25, 2009 at 11:33pm
isn't the revenue = cost per month x number of customers?
didn't I define the "number of customers"
as 5000 + 500n
but x was 20n which gave me n = 20x
I then subbed that in 5000 + 500n
to get 15000  500x as I showed above step by step.

math  PurduePete, Friday, October 14, 2011 at 11:12pm
The above is all correct except for one mistake. x(15,000500x) is not 15,000500x^2 but rather 15,000x500x^2. The x was not properly distributed in the original answer.
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