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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Average cost Suppose the total cost of producing x units of a product is given by

C ( x ) = 4500 + 120 x + 0.5 x 2 dollars

(a) Find any asymptotes of the average cost function C ¯ ( x ) = C ( x ) / x .

(b) Graph the average cost function.

(a)

To determine

To calculate: The asymptotes of the average cost function C¯(x)=C(x)x where C(x)=4500+120x+0.05x2.

Explanation

Given Information:

The provided cost function is C(x)=4500+120x+0.05x2.

Formula used:

A vertical asymptote of a function f(x) is a line x=a such that f(a)=.

A vertical asymptote of a rational function h(x)=f(x)g(x) is x=a where g(a)=0 and f(a)0.

A horizontal asymptote of a function f(x) is a line y=b such that limxf(x)=b or limxf(x)=b.

Calculation:

Consider the provided cost function is C(x)=4500+120x+0.05x2.

The average cost function is C¯(x)=C(x)x.

C¯(x)=4500+120x+0.05x2x=4500x+120xx+0.05x2x=4500x+120+0.05x

Thus, the average cost function is C¯(x)=4500x+120+0

(b)

To determine

To Graph: The average cost function C¯(x)=C(x)x where C(x)=4500+120x+0.05x2.

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