Question

The total revenue for stan's estates llc is given as function R(x)=200 x - 0.4x^2 , where x is the number of apartments rented . what number of apartments rented produces the maximum revenue ? ___apartments

Answer 1

We will obtain maximum revenue when 250 apartments are rented.

Step-by-step explanation

The total revenue is given in function form as

R(x) = 200x - 0.4x²

x = number of apartments rented

We are then asked to find the number of apartments rented (x) that produces the maximum revenue.

For this, we know that at maximum point for any function, the first derivative is 0 and the second derivative is negative.

So, to find the x when the function is maximum, we just find the first derivative and equate it to 0.

R(x) = 200x - 0.4x²

First derivative

(dR/dx) = 200 - 0.8x

200 - 0.8x = 0

0.8x = 200

Divide both sides by 0.8

(0.8x/0.8) = (200/0.8)

x = 250 apartments rented

Second derivative

(d²R/dx²) = -0.8

Negative, proving that this is truly the maximum point for this function.

Hope this Helps!!!