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Mathematics-Online problems:

Interactive Problem 1036: Maximization of the Revenue of a Soccer Stadium

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A soccer stadium in Scotland has $ 60\,000$ seats. Due to the economical behaviour of its population, the number $ n$ of the tickets sold for a home game is exclusively determined by their price $ p$ (in $ \pounds$):

$\displaystyle n=100\,000 -2000\, p\,. $

a) At which price $ p$ will the revenue $ R$ reach its maximum?
b) For which interval of prices $ p_{\min} \leq p \leq p_{\max}$ is the revenue $ \geq \pounds \ 1,200,000$?
c) Which price maximizes the revenue, if tickets not sold previously were sold on the day of the match at half price to students (subject to sufficient demand)?


Answer:

a) $ p$ =
  $ R$ =
b) $ p_{\min}$ =
  $ p_{\max}$ =
c) $ p$ =
  $ R$ =

(all results in $ \pounds$)


   

(From: Day of Mathematics 2006)
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  automatically generated: 2/ 6/2018