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Revenue Optimization problem

  1. May 8, 2008 #1
    [SOLVED] Optimization problem

    1. The problem statement, all variables and given/known data
    A baseball team plays in the stadium that holds 60000 spectators. With the ticket price at 8 the average attendence has been 24000. When the price dropped to 7, the average attendence rose to 30,000.
    a) find the demand function p(x), where x is the number of spectators (assume p(x) is linear p(x)=
    b) How should the ticket price be set to maximize revenue?


    2. Relevant equations



    3. The attempt at a solution
    a) I figured out that the demand function was: 8-(1/6000)(x-24000)
    b) I tried to use the revenue formula:; by taking the derivative of the demand function which is: 12-(12,000x/6000[tex]^{}2[/tex])
    and then I set that equal to zero and tried to solve for X, which is: 36,000
    So, now I don't know how to use the above information to calculate the price of the ticket. any suggestions?
     
    Last edited: May 8, 2008
  2. jcsd
  3. May 8, 2008 #2
    So x = 36,000 is a critical number of the revenue function [itex]r(x) = xp(x) = 12x - x^2 / 6000[/itex]. What does that tell you about r(x) at x = 36,000? What does that tell you about p(x)?
     
  4. May 8, 2008 #3
    I plugged in the x=36,000 into the demand function and I got $6.00 as the answer, I verified it and it is correct.
    Thanks, I appreciate your help.
     
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