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!!

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- anonymous

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

http://bit.ly/eylJbx

- anonymous

thanks so much!!!

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- anonymous

Welcome :)

- anonymous

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

- anonymous

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

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