Question

The total revenue for Fred's Estates LLC is given as the function R(x)=400x−0.5x² , where x is the number of apartments filled. What number of apartments filled produces the maximum revenue?

A) 400
B) 200
C) 0
D) 800

Answer 1

A) 400

Step-by-step explanation:

To find the number of apartments filled that produces the maximum revenue, we can

use the vertex formula for a quadratic function ac2 -F bc -F c, given by = —

In this case, the revenue function is R(c) —0.5c2 + 400% where a = 0.5 and b = 400.

The vertex formula for the maximum occurs at c

1

400

Therefore, the correct answer is:

A) 400

Answer 2

The number of apartments filled that produces the maximum revenue is 400.

Step-by-step explanation:

To find the number of apartments that produces the maximum revenue, we need to find the maximum point on the revenue function. The revenue function is given by R(x) = 400x - 0.5x^2. To find the maximum point, we can take the derivative of the revenue function and set it equal to zero. The derivative of R(x) is dR/dx = 400 - x. Setting this derivative equal to zero and solving for x gives x = 400. Therefore, the number of apartments filled that produces the maximum revenue is 400.