Results 1 to 4 of 4

Math Help - Having a lot of trouble understanding optimization

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Having a lot of trouble understanding optimization

    Hey, all. I'm new here. I have been struggling very much to get this problem figured out, and I am just completely stuck.

    I will type it out:

    A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket price set at $12, average attendance at a game has been 11,000. A market survey indicates that for each dollar the ticket price is lowered, average attendance will increase by 1000. How should the owners of the team set the ticket price to maximize revenue from ticket sales?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    Let R be the revenue and x be the decrease in price of each ticket)

    Then R = (12-x)(11000+1000x) = 132000 + 1000x - 1000x^2

    \frac{dR}{dx} = 1000-2000x

    Solve for x to make the equation 0 and you will have the value of x that gives maximum revenue. Then the cost of each ticket is $(12-x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    3
    Quote Originally Posted by nzmathman View Post
    Let R be the revenue and x be the decrease in price of each ticket)

    Then R = (12-x)(11000+1000x) = 132000 + 1000x - 1000x^2

    \frac{dR}{dx} = 1000-2000x

    Solve for x to make the equation 0 and you will have the value of x that gives maximum revenue. Then the cost of each ticket is $(12-x)
    Wonderful. Thank you so much for this! Yet even so, I get the feeling that there is some sort of formula or concept that goes behind this. It seems very structured and well thought out. Is there some sort of concept or formula that goes behind a problem like this?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    Well for a problem like this you need to think and find a formula for what you are being asked to maximise or minimise. In this case (12-x) is the decreased price of each ticket, and (11000+1000x) is the average number of spectators for a particular value of x. So the revenue must equal these two numbers multiplied...

    For maxima/minima one always differentiates the formula and equates to 0. If you are familiar with parabolas you will recognise that our formula in this question is an upside down parabola and has a maximum value when the derivative is 0. In other instances a formula has maxima and minima so you need to do extra work to find which is which
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Trouble understanding Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 29th 2010, 11:37 PM
  2. Having some trouble understanding ideals...help?
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 27th 2010, 05:38 PM
  3. Trouble understanding combinations
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 13th 2010, 02:05 PM
  4. Having trouble understanding this example
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: March 20th 2009, 11:33 PM
  5. Replies: 1
    Last Post: January 6th 2009, 06:39 PM

Search Tags


/mathhelpforum @mathhelpforum