Question

campground charges $20 to camp for the night. They average 43 groups renting campsites each night. A recent survey indicated that for every $2 decrease in the nightly price, the number of campsites rented increases by 7. What price will maximize nightly revenue? Make sure to include your equation with your work.

Answer 1

To maximize nightly revenue, we need to find the price associated with the maximum number of campsites rented. By representing the relationship between price and the number of campsites rented with an equation and finding the vertex of the quadratic function, we can determine that the price that will maximize nightly revenue is $20.

Step-by-step explanation:

To determine the price that will maximize nightly revenue, we need to find the price associated with the maximum number of campsites rented. Let's define the price as P and the number of campsites rented as N. According to the information given, for every $2 decrease in price, the number of campsites rented increases by 7. This can be represented by the equation:

N = 43 + (P-20)/2 * 7

To maximize revenue, we need to find the value of P that maximizes N. We can do this by finding the vertex of the quadratic function representing N in terms of P.

Using the formula for the x-coordinate of the vertex of a quadratic function, we have:

P = -b/(2a) = -(-20)/(2(7/2)) = 20

Therefore, the price that will maximize nightly revenue is $20.