The total revenue for Jane's Vacation Rentals is given as the function R(x)=300x−0.25x^2, where x is the number of rooms filled. What number of rooms filled produces the maximum revenue?

Question

this is for my college algebra class please help

Answer 1

This function is a parabola opening downward. You can find where it crosses the x-axis by setting it equal to zero and solving for x.

-x^2/4 + 300 x = 0 --> (x-1200)x = 0

The x-axis crossings are at zero and x = 1200. The maximum x value is half way between these two points, or

x = 600. In other words, the axis of symmetry is -b/2a = -300/(2(-1/4)) = 600.

Answer 2

The number of room is on the x-axis. So we need to find the axis of symmetry.

x = -b/2a

where b = 300, a = -0.25 from the original equation.

x = -(300) / (2x(-0.25))

x = -300/(-0.5)

x = 600 rooms