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 = 20-n
number of customers = 5000 + 500n
but you want 20-n = x
so n = 20-x
and 5000 + 500n
= 5000 + 500(20-x)
= 5000 + 10000 - 500x
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 15000-500x 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 20-n which gave me n = 20-x
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(15,000-500x) is not 15,000-500x^2 but rather 15,000x-500x^2. The x was not properly distributed in the original answer.
Answer This Question
More Related Questions
- Accounting - The City of Mirada wants to offer cable television to its residents...
- Math - Company A charges $11 per month plus $0.05 per minute, while company B ...
- Math - A cable TV company charges $24.95 per month for basic service and $6.95 ...
- Statisitics - Identify the population, and the sample in each of the following...
- MATH (PROBABILITY) - According to Nielsen Media Research, approximately 52% of...
- statistics - If 86% of households have cable television and three households are...
- math - ahmed works as an electrician. When he installs television cables in new ...
- Finance - Assume that you have a balance of $5000 on your Visa credit card and ...
- Algebra - A phone company charges $30 per month for a long distance plan plus a ...
- Math - A random survey of 500 households determines that 20% of the households ...