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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.

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