Math

Assume that it costs Apple approximately

C(x) = 36,100 + 100x + 0.01x^2

dollars to manufacture x 30-gigabyte video iPods in a day.

How many iPods should be manufactured in order to minimize average cost?

What is the resulting average cost of an iPod? (Give your answer to the nearest dollar.)

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asked by Jerry
  1. cost per unit = cpu = C(x) / x
    = 36,100/x + 100 +.01 x

    d cpu/dx = 0 at min
    = -36,100/x^2 + .01
    .01 x^2 = 36,100
    x^2 = 3,610,000
    x = 1900 units
    now go back and get cpu
    = 36,100/1900 + 100 + .01(1900)
    = 2019

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    posted by Damon
  2. d cpu/dx = 0 at min
    = -36,100/x^2 + .01
    .01 x^2 = 36,100
    x^2 = 3,610,000
    x = 1900 units
    now go back and get cpu
    = 36,100/1900 + 100 + .01(1900)
    What is the resulting average cost of an iPod?
    138

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