The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so that the avera

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The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $21?

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Tài Đức 2 months 2021-08-04T19:02:37+00:00 1 Answers 1 views 0

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    2021-08-04T19:04:24+00:00

    Answer:

    The least number of items to produce is 41

    Step-by-step explanation:

    Average Cost

    Given C(x) as the cost function to produce x items. The average cost is:

    \displaystyle \bar C(X)=\frac{C(x)}{x}

    The cost function is:

    C(x) = -20x+1681

    And the average cost function is:

    \displaystyle \bar C(X)=\frac{-20x+1681}{x}

    We are required to find the least number of items that can be produced so the average cost is less or equal to $21.

    We set the inequality:

    \displaystyle \frac{-20x+1681}{x}\le 21

    Multiplying by x:

    -20x+1681 \le 21x

    Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.

    Adding 20x:

    1681 \le 21x+20x

    1681 \le 41x

    Swapping sides and changing the sign:

    41x \ge 1681

    Dividing by 41:

    x\ge 41

    The least number of items to produce is 41

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