Mathematics: An accessories company finds that the cost, in dollars, of producing x belts is given by Upper C (x )equals 720 plus 35 x minus 0.063 x squared. Find the rate at which average cost is changing when 180 belts have been produced.

An accessories company finds that the cost, in

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19.01.2022

The average cost of belt is decreasing at a rate 0.085 dollars per belt when 180 belts have been produced.

Step-by-step explanation:

We are given the following in the question:

Cost function:

C(x) = 720 + 35x-0.063x^2

where x is the number of belts.

Average cost =

$A(x) = \dfrac{C(x)}{c} = \dfrac{720 + 35x-0.063x^2}{x}\\\\A(x) = \dfrac{720}{x} + 35 -0.063x$

Rate of change of average function:

$\dfrac{d(A(x))}{dx} = \dfrac{d}{dx}( \dfrac{720}{x} + 35 -0.063x)\\\\\dfrac{d(A(x))}{dx} = \dfrac{-720}{x^2}-0.063$

Change in average cost when 180 belts have been produced

$\dfrac{d(A(180))}{dx} = \dfrac{-720}{(180)^2}-0.063 = -0.085$

Thus, the average cost of belt is decreasing at a rate 0.085 dollars per belt when 180 belts have been produced.

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