Results 1 to 8 of 8

Math Help - optimization and revenue problem

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    15

    optimization and revenue problem

    A baseball team plays in a stadium that holds 62000 spectators. With the ticket price at $12 the average attendence has been 26000. When the price dropped to $11, the average attendence rose to 31000. Assume that attendence is linearly related to ticket price.


    What ticket price would maximize revenue?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by eawolbert View Post
    A baseball team plays in a stadium that holds 62000 spectators. With the ticket price at $12 the average attendence has been 26000. When the price dropped to $11, the average attendence rose to 31000. Assume that attendence is linearly related to ticket price.


    What ticket price would maximize revenue?
    we have a linear relationship, and we are given two points.

    let the ticket price be plotted on the x-axis and the attendance on the y-axis. we have the points (12,26000) and (11,31000). we can use this to get the equation of the line that relates the ticket price, P, and the attendance, A. This will be your constraint equation (you know what that is, right?)

    Now, the revenue, R, is given by:

    R = PA ............the objective equation

    you want to maximize R. You must find its derivative and set it to zero and solve for the appropriate quantity of whatever variable you use. of course, you use the constraint equation to solve for one variable in terms of the other and then plug in the expression in the objective equation so that you get the equation in one variable. then proceed to integrate

    can you continue?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    15
    ok now i'm totally lost can you explain it to me a little more detailed please. thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by eawolbert View Post
    ok now i'm totally lost can you explain it to me a little more detailed please. thanks
    ok, we can do this step by step. start by finding the equation of the line between those two points. do you know how to do this?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2008
    Posts
    15
    I tried doing that but got a really weird equation. I got -5000x+86000
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by eawolbert View Post
    I tried doing that but got a really weird equation. I got -5000x+86000
    That is correct. so you have

    A = -5000P + 86000 ....................................(1)

    now the revenue is the cost of each ticket times the number of tickets sold, so,

    R = PA .............................................(2)

    but we need to maximize this. to do that, we need to differentiate. this is a problem, since we have two variables. But we're in luck. from equation (1), we can write one variable in terms of another. so plug in (1) into (2), we get:

    R = P(-5000P + 86000)

    => R = -5000P^2 + 86000P

    now this last equation is what you want to maximize. can you continue?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2008
    Posts
    15
    Awesome. Great that's the part I was missing. thanks a lot
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by eawolbert View Post
    Awesome. Great that's the part I was missing. thanks a lot
    you're welcome, dude(?)!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization of Revenue
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 29th 2011, 03:39 PM
  2. revenue problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 11th 2010, 05:46 PM
  3. Revenue problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 11th 2009, 01:56 PM
  4. Replies: 1
    Last Post: November 24th 2009, 12:43 PM
  5. Replies: 1
    Last Post: November 18th 2009, 07:16 PM

Search Tags


/mathhelpforum @mathhelpforum