An average of 40000 people visit Riverside Park each day in the summer. The park charges $21.00 for admission. Consultants predict that for each $1.00 increase in the entrance price, the park would lose an average of 2500 customers per day.
I need to find a formula for the daily revenue. Someone help please!!

Question

An average of 40000 people visit Riverside Park each day in the summer. The park charges $21.00 for admission. Consultants predict that for each $1.00 increase in the entrance price, the park would lose an average of 2500 customers per day. 
 I need to find a formula for the daily revenue. Someone help please!!

anonymous · Answer

people = 40000 - 2500(x)
x is the increase in price

price = 21 + x

Revenue = people * price

 = (40,000 - 2500x) * (21 + x)
 = -2500x^2 - 12500x + 840000

anonymous · Answer

http://bit.ly/eylJbx

anonymous · Answer

thanks so much!!!

anonymous · Answer

Welcome :)

anonymous · Answer

Hey theres a second part which asks : What ticket price maximizes the revenue from ticket sales

anonymous · Answer

Okay to maximize revenue you need to take the derivative and set it equal to 0.  If you look at the graph I posted, when the derivative is 0, that is the maximum amount that can be made.  This is assuming though that for every $1 DECREASE in price, the number of people goes up by 2500.

The derivative of -2500x^2 - 12500x + 840000
 = -5000x - 12500
5000x = -12500
x = -2.5

Since the x is a negative number, that means the price must be decreased by $2.50 to reach the maximum revenue.

So 21 - 2.5 = $18.50
2.50 * 2500 = 6250
$18.50 * 46,250 = $855,625