1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Maximizing Revenue
  1. Maximizing Revenue ahh (Replies: 11)

  2. Maximizing profit (Replies: 3)

  3. Maximize profit (Replies: 2)

Loading...