## The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost les

Question

The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?

A) ( 2, infinit)

B) (0,2)

C) (-infinit,0) U (2,infinit)

D) (- infinit,0] U [2,infinit)

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2021-07-22T21:08:22+00:00
2021-07-22T21:08:22+00:00 1 Answers
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## Answers ( )

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Answer:A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don’t think about it

Step-by-step explanation:We want …

C(x)/x < 100

(20x +160)/x < 100

20 +160/x < 100 . . . . . separate the terms on the left

160/x < 80 . . . . . . . subtract 20

160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

x > 2 . . . . . . simplify

In interval notation this is

(2, ∞). matcheschoice A__

Technically (mathematically), we also have …

160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one._____

Comment on the solutionSince we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.