Suppose that 2,500 people are interested in attending ElvisLand.Once a person arrives at ElvisLand, his or her demand for rides is given by x  max3  p, 0 , where p is the price per ride.There is a constant marginal cost of $2 for providing a ride at ElvisLand.ElvisLand charges a profit-maximizing two-part tariff, with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?

A) $2 per ride and $3 for admission
B) $0 per ride and $2.50 for admission
C) $2 per ride and $.50 for admission
D) $0 per ride and $1 for admission
E) $3 per ride and $3 for admission

To find the profit-maximizing prices, we need to use the formula:
Profit = (Price per ride - Marginal Cost) * Quantity of rides + Price for admission * Quantity of visitors
Let's start by finding the demand function for rides. The function provided is:
x = min{10, 3p}
Since we know the demand function, we can find the quantity of rides by plugging it into the function:
Quantity of rides = min{10, 3p}
Next, we need to find the quantity of visitors. We know that 2,500 people are interested in attending, but not all of them may decide to come depending on the admission price. Let's assume that if admission is free, all 2,500 people show up. Then, if admission is charged at a price of a, some people will drop out, and the number of visitors will be:
Quantity of visitors = 2,500 - a/0.5
Now we can plug in the appropriate values into the profit equation:
Profit = (p - 2) * min{10, 3p} + a(2,500 - a/0.5)
To maximize profit, we take the derivative with respect to both p and a, and set them equal to zero:
dProfit/dp = 0 ---> p = 2/3
dProfit/da = 0 ---> a = 1000
Therefore, the profit-maximizing prices are $2 per ride and $0.50 for admission.