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Problem for calculus

  1. Sep 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Currently 2000 people attend performances of The Sound of Music if tickets cost $40. Expenses are $8 per person in attendance for each performance. For each $2 decrease in the ticket price, 200 more people attend. Calculate the ticket price that produces maximum profit.

    2. Relevant equations

    don't really know of relevant equations besides derivatives.

    3. The attempt at a solution

    So i'm struggling to solve this one, i've been trying to use another similar problem to help me solve this and so i have come up with 2 functions for it.

    2000+200x for how much people will come in
    40-2x for the minimum price for the fare
    now i don't know where to put $8 and well i just can't figure out the main function so i can come up with a derivative and solve for x.
  2. jcsd
  3. Sep 21, 2010 #2


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    Staff: Mentor

    What are expenses when n people attend?

    What is profit?
  4. Sep 21, 2010 #3
    well i think the expences will be 8 dollars per person so 8(2000+200x)
    the profit before expenses will be........ (40-2x)(2000+200x) ??
    so overall profit will be mmm P = (40-2x)(2000+200x)-8(2000+200x) ???

    man, optimization problems are so tricky.....but i can't give up, worth alot of marks hahaha.
  5. Sep 22, 2010 #4


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    Staff: Mentor

    I can be missing something, but so far looks OK to me.
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