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Homework Help: Maximizing Revenue

  1. Jan 6, 2010 #1
    1. The problem statement, all variables and given/known data
    An average of 20 000 people visit the Lakeside Amusement Park each day in the summer. The admission fee is $25.00. Consultants predict that, for each $1.00 increase in the admission fee, the park will lose an average of 750 customers a day. Determine the function that represents the projected daily revenue if the admission fee is increased AND estimate the ticket price that will maximize function.


    2. Relevant equations
    I figured out the equation of the revenue, which I'm sure is correct. It is:

    D(n) = (25.00 + 1.00n)(20 000-750n)

    let n represent the number of times the price increases.



    3. The attempt at a solution
    However, I did not understand the second question, do you have to lower the ticket price to maximize revenue? Also, can anyone explain an fast way to determine a maximum revenue, because my method involves choosing random numbers and plopping them into the equation until I find a good value?

    Thanks everyone! :)
     
  2. jcsd
  3. Jan 6, 2010 #2

    Char. Limit

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    Gold Member

    There are two ways to do this: one involves calculus, so I won't cover that, and the other involves the graph.

    Just take a look at the graph and ask yourself, when does the graph appear to max out?

    Also, a little personal tip: in a quadratic equation, the maximum is usually halfway between the two zeroes, at least in my experience.

    Sorry if I spoke too much.
     
  4. Jan 6, 2010 #3
    Congrats, you have the right revenue function, just expand it so it is quadratic. There are three methods:

    1. Calculus: This is the easiest method(this question seems to be a preview of differential calculus).

    2. Graph it.

    3. Plug in different numbers and "zoom-in" into the maximum.

    4. Your teacher may have told you the formula for finding the maximum of a quadratic function, I remember our Algebra II teacher gave us the formula.
     
  5. Jan 7, 2010 #4
    I'm not learning Calc until next semester, but I just graphed it and plugged in some values.
    Thanks guys!
     
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