How Is the Revenue Function R(x) = 500x(30-x) Derived for the Cable Firm?

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Homework Help Overview

The discussion revolves around deriving the revenue function R(x) for a cable television firm based on customer behavior in response to pricing changes. The context includes the current pricing structure and customer base, as well as insights from a marketing survey.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the derivation of the revenue function R(x) = 500x(30-x) and specifically questions the origin of the number 30 in the function. Some participants clarify that 30 is derived from the relationship between price increases and customer retention.

Discussion Status

The discussion is active, with participants providing insights into the assumptions behind the revenue function. Clarifications have been offered regarding the interpretation of the data, but no consensus has been reached on the broader implications of the function.

Contextual Notes

Participants are exploring the implications of customer behavior in relation to pricing changes, with some noting that the function's parameters are based on specific market research findings. There is an acknowledgment of the assumptions made in the problem setup.

Bitter
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The problem is this

A cable television firm presently serves 5000 households and charrges 20 dollars per month. A marketing survey indicates that each decrease of 1 dollar in the monthly charge will result in 500 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars.

Determine the revenue function R

The back of the book says
R(x)=500x(30-x)

I don't see where the 30 comes from, can anyone tell me?
 
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30 is given information. It is obtained by observing that increasing the monthly fee by 10 dollars from 20 would result in 0 households with the service.
 
ah! Thank you. I feel stupid now. how could i overlook that.
 
Well, since my new problem relates to basic functions, I figured I'll just reuse to this topic.

This isn't exactly homework, but I just have a question.

Why does (x^2+1)(x-1)/(x^2 + 1)(x-2) not have a hole in the graph despite having a common factor?
 
Because x2+ 1 is never 0.
 

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