Question

Rogers Place can hold a maximum number of 18,500 fans for an Edmonton Oilers hockey game. Based on historical data, at an average ticket price of $180, an average of 15,000 fans buy a ticket and attend the game. For each $3 that the average ticket price is increased (or lowered), 300 fans less (or more) buy a ticket.

(a) Let x(p) be the number of fans attending a game at an average price p. Determine the function x(p).

(b) Determine the revenue function and the intervals where it is decreasing or increasing?

(c) Based on your answer in part (b), what is the average ticket price at which the revenues is locally maximized?

Answer 1

a)

Here,

Given:

Put in (1)

Also

Put in (1)

Substract (2) from (3)

Using (2)

b)

We know ,

Total revenue = Price * no of fans

So check decreasing function is

It is increasing in

And , Decreasing in

c)

Differentiating (4) in b is

Differentiating (5)

So, find the max

Put R'(P)=0

-200P+33000=0

P=165>0

And R''(P)=-200<0

So,

Hence it is max when price is $165