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Demand and revenue question: help?

  1. Mar 6, 2013 #1
    A store has been selling 200 MP3 players a week at 300$ each. A market survey indicates that for each $10 rebate offered to the buyers, the number of sets sold will increase by 20/week.
    a) find the demand function and the revenue function.
    b) How large a rebate should the store offer to maximize its revenue?

    a) Let n be the # of price increases
    Let x be the number of MP3 players
    Let p be the price of 1 MP3 player

    x= 200 + 20n
    x-200/20= 20n/20
    1) n=x-200/20

    2) d= 300-10n

    sub 1 into 2
    d(x)= 300-10(x-200/20)
    d(x)= 400-x/2

    r(x) = xd(x)
    = 400 - x^2/2

    b) after doing these steps...I am not sure what to do from here.
    Can someone explain how to approach this step?

    Thank you so much!
     
  2. jcsd
  3. Mar 6, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    I think n is the number of price reductions, otherwise an increased price would increase the number of sold MP3 players.
    Do you mean (x-200)/20=20n/20?
    As x-200/20 = x-10.

    The last line is wrong.
     
  4. Mar 6, 2013 #3

    Ray Vickson

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    Science Advisor
    Homework Helper


    I think you should start again, and be more careful and more explicit. For example, you could say something like:
    S = number of MP3 players sold (per week) (was this your d?)
    r = rebate (in $) (probably, your n)
    p = selling price per player (in $)
    Now give equations for S and p in terms of r. Then use those expressions to get revenue R ($ per week) in terms of the rebate, r. The result will be quite different from what you wrote.
     
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