Question 1024931: A hockey team plays in an arena that has a seating capacity of
15,000 spectators. With the ticket price set at $50, average attendance
at recent games has been 10500. A market survey indicates that for
each dollar the ticket price is lowered, the average attendance increases
by 100.
(a) Find a function that models the revenue in terms of ticket price.
(b) Which attendance will give the maximum revenue? Justify your
answer
I did ticket=x
amount price is lowered: 50-x
increase in attendence=100(50-x)
attendance: 10500+100(50-x)=15500-100x
revenue=ticket price*attendemce
R(x)=x(15500-100x)=15500-100x^2
i am not sure how to do the second part all i know is if i use x=-b/2a i can find ticket price that maximizes revenue however they are asking for attendance which maximizes revenue. Thanks a lot for your time!
Answer by JoelSchwartz(130)   (Show Source):
You can put this solution on YOUR website! x=the number of times that the ticket price is reduced by one dollar
y=the price of each ticket
y=50-x
z=the number of people attending the game
z=10,500+100x
y*z=the total revenue for that game
y*z=(50-x)(10,500+100x)
the maximum revenue for one game is when the attendance is 10,500 people.
The reason why is that the ticket price goes down when there are more people attending the game.
50*10,500=525,000
49*10,600=519,400
48*10,700=513,600
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