A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machin

Question

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If X machines are made, then the unit cost is given by the function C(x)=0.6x^2-168x+30,389. What is the minimum unit cost?
Do not round your answer.

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Bình An 5 years 2021-07-19T03:57:01+00:00 1 Answers 118 views 0

Answers ( )

  1. Jezebel
    0
    2021-07-19T03:58:12+00:00
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    Answer: \$18,629

    Step-by-step explanation:

    Given

    The unit cost is given by

    C(x)=0.6x^2-168x+30,389

    find the derivative of the unit cost and equate it to zero to obtain the minimum value

    C'(x)=0.6\times 2x-168\\\Rightarrow 0.6\times 2x-168=0\\\Rightarrow 1.2x=168\\\\\Rightarrow x=\dfrac{168}{1.2}\\\\\Rightarrow x=140

    Substitute 140 for x in the cost function, we get

    C(140)=0.6[140]^2-168(140)+30,389\\C(140)=11,760-23,520+30,389\\C(140)=\$18,629

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