Results 1 to 4 of 4

Math Help - Optimization problem

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    21

    Optimization problem

    An amateur theater company offers a group discount for its evening performances. For every person in a group of 30 or more, the ticket price decreases by $1.50 from the regular price of $24.00. Determine the size of group that maximizes revenue.

    How do I go about solving this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2009
    Posts
    177
    The question does not make sense. If you need to be 30 in a group in order to receive a discount, then any group size below 30 is going to maximize the revenue as long as the theater gets filled.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    21
    Quote Originally Posted by Mondreus View Post
    The question does not make sense. If you need to be 30 in a group in order to receive a discount, then any group size below 30 is going to maximize the revenue as long as the theater gets filled.
    Well, considering the answer that they give you on the book is '30' then what you are saying makes sense. Revenue starts decreasing when they sell more than 30 tickets so 30 is the critical point in which revenue is maximized.

    Could you help me prove this mathematically though?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2009
    Posts
    177
    If this is how the question was originally phrased, then I'd still say that it does not make sense to be honest.

    If the ticket price decreases with $1.50 for every person in a group of 30 or above, then the ticket price would be less than zero for every group of 30 or above: 24-1.5\cdot 30 = -21

    You can express it mathematically with the help of a shifted Heaviside step function, but I seriously doubt that the original question was phrased like this.
    Last edited by Mondreus; May 21st 2011 at 04:11 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization Problem?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 1st 2010, 07:34 AM
  2. Optimization Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 8th 2009, 11:37 PM
  3. Optimization problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 15th 2008, 10:29 AM
  4. help!!!- optimization problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 13th 2008, 05:59 PM
  5. Optimization Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 16th 2008, 01:21 PM

Search Tags


/mathhelpforum @mathhelpforum