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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Tryphena 2 weeks 2021-07-22T21:08:22+00:00 1 Answers 4 views 0

Answers ( )

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    2021-07-22T21:09:59+00:00

    9514 1404 393

    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, ∞).   matches choice 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 solution

    Since 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.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )