Question

The total revenue for Fred's Estates LLC is given as the function R(x)=200x−0.4x2, where x is the number of rooms booked. What number of rooms booked produces the maximum revenue?

Answer 1

Answer:

250 rooms gives R(250) = 25000

Step-by-step explanation:

R(x)=200x−0.4x^2

Set derivative to zero to find min or max.

dR(x)/dx = 200 - 0.8x

200 - 0.8x = 0

x = 250

R(250) = 25000

R(249) = R(251) = 24999.6

Solution is a maximum.

Answer 2

The number of rooms booked to produce maximum revenue is required.

The number of rooms booked to produce the maximum revenue is 250.

The revenue function is

$R(x)=200x-0.4x^2$

Differentiating with respect to x we get

$R'(x)=200-0.8x$

Equating with zero

$0=200-0.8x\\\Rightarrow x=\dfrac{-200}{-0.8}\\\Rightarrow x=250$

Double derivative of the function is

$R''(x)=-0.8x$

Substituting the value of $x=250$

$R''(250)=-0.8\times 250=-200$

Since, it is negative the maximum value of x will be 250.

The number of rooms booked to produce the maximum revenue is 250.

Learn more:

https://brainly.com/question/24896699

https://brainly.com/question/2150186