A certain electronics manufacturer found that the average cost C C to produce x DVD/Blu- ray players can be found using the equation C = 0.0

Question

A certain electronics manufacturer found that the average cost C C to produce x DVD/Blu- ray players can be found using the equation C = 0.03 x 2 − 5 x + 700 C=0.03×2-5x+700. What is the minimum average cost per machine and how many DVD/Blu-ray players should be built in order to acheive that minimum?

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Mackenzie 2 weeks 2021-09-11T02:46:48+00:00 1 Answer 0

Answers ( )

    0
    2021-09-11T02:47:50+00:00

    Answer:

    83,491.67 dollars

    Step-by-step explanation:

    Given that a certain electronics manufacturer ound that the average cost C C to produce x DVD/Blu- ray players can be found using the equation  C=0.03x^2-5x+700

    To find the minimum average cost per machine we can use derivative test.

    we find first and second derivative.

    If for a particular value of x first derivative is 0 and second derivative is positive, then that x satisfies the minimum cost criteria.

    C=0.03x^2-5x+700\\C'(x) = 0.06x-5\\C"(x) = 0.06>0

    Second derivative is always positive

    I derivative =0 gives

    x=5/0.06 \\=83.33\\~83

    For 83 players the cost would be minimum

    Minimum cost = 0.03(83)^2-5(83)+700\\=491.67

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