Question

The total revenue for Jane's Vacation Rentals is given as the function R(x)=400x−0.4x2

, where x is the number of apartments booked. What number of apartments booked produces the maximum revenue?

Answer 1

To find the number of apartments booked that produces the maximum revenue, we can determine the vertex of the quadratic function R(x) = 400x - 0.4x^2. The x-coordinate of the vertex represents the number of apartments that will maximize the revenue.

The vertex of a quadratic function in the form ax^2 + bx + c can be found using the formula x = -b / (2a).

In this case, a = -0.4, b = 400, and c = 0.

Using the formula, we can calculate the x-coordinate of the vertex:

x = -b / (2a)
= -(400) / (2 * (-0.4))
= -400 / (-0.8)
= 500

Therefore, the number of apartments booked that produces the maximum revenue is 500.