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