# math

posted by .

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 -

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
= 15000-500x

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 -

why do u multiply everything by x at the end? and what is 15000-500x equal to? the number of costumers?

• math -

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 -

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.

## Similar Questions

1. ### Accounting

The City of Mirada wants to offer cable television to its residents in 2009. The city has approached a company called CableVision to run its cable operations. After negotiating with key parties, CableVision has made the following agreements: …
2. ### math

You operate a gaming Web site, where users must pay a small fee to log on. When you charged \$4 the demand was 510 log-ons per month. When you lowered the price to \$3.50, the demand increased to 765 log-ons per month. (a) Construct …
3. ### Algebra

You operate a gaming Web site, where users must pay a small fee to log on. When you charged \$3 the demand was 520 log-ons per month. When you lowered the price to \$2.50, the demand increased to 780 log-ons per month. (a) Construct …
4. ### Algebra

As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of \$2,600. With this pricing …
5. ### algebra

A club currently has 300300 members who pay \$ 400\$400 per month for membership dues. The​ club's board members want to increase monthly revenue by lowering the monthly dues in hopes of attracting new members. A market research …
6. ### Algebra

A club currently has 300 members who pay \$ 400 per month for membership dues. The​ club's board members want to increase monthly revenue by lowering the monthly dues in hopes of attracting new members. A market research study …
7. ### Math

The manager of a home electronics store is considering repricing a new model of digital camera. At the current price of \$680 the store sells about 70 cameras each month. Sales data from other stores indicate that for each \$20 decrease …
8. ### Math

Company A charges \$11 per month plus \$0.05 per minute, while company B charges \$0.15 per minute with no monthly charge. For how many minutes will the monthly cost be the same?
9. ### quantitative methods II

A firm that produces car components has a fixed costs of \$ 40,000 per month and a variable cost of \$ 24 per component.it sells its product at a price of \$ 44 per component,regardless of the number of units sold. (i)find the break-even …
10. ### math

Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly …

More Similar Questions