Question

The​ revenue, in​ dollars, from the sale of x belts is given by R(x)=40x^4/7 Find the rate at which average revenue is changing when 545 belts have been produced
When 545 belts have been produced and​ sold, the average revenue is changing at --------- :1) dollars per belt 2) belts per dollar for each additional belt
​(Round to four decimal places as needed. Do not include the​ $ symbol in your​ answer.)

Answer 1

Answer:

The average revenue is decreasing at a rate of 0.0021 dollars per belt when 545 belts have been produced and​ sold.

Step-by-step explanation:

We are given the following in the question:

$R(x) = 40x^{\frac{4}{7}}$

where R(x) is the revenue function and x is the number of belts.

Average revenue:

$\bar{R}(x) = \dfrac{R(x)}{x} = \dfrac{40x^{\frac{4}{7}}}{x} = 40x^{\frac{-3}{7}}$

Rate of change of average revenue:

$\dfrac{d\bar{R}(x)}{dx} = \dfrac{d}{dx}(40x^{\frac{-3}{7}}) = \dfrac{-120}{7}x^{\frac{-10}{7}}$

Putting x = 545

$\dfrac{d\bar{R}(545)}{dx} = \frac{-120}{7}(545)^{\frac{-10}{7}} = -0.0021$

Thus, when 545 belts have been produced and​ sold, the average revenue is decreasing at a rate of 0.0021 dollars per belt.