A baseball team plays in a stadium that holds 50000 spectato

A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the average attendance has been 19000. When the price dropped to $5, the average attendance rose to 25000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue? $

Solution

Let , A denote attendance and T be ticket price so

A=kT+c

Using given data

19000=8k+c

25000=5k+c

k=-2000,c=35000

Revenue=AT=-2000T^2+35000T=-2000(T^2-35T/2)=-2000(T-35/4)+2000*35^2/16

So ticket price to maximize revenue is

T=35/4 =$8.75