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14 September, 03:49

1) The cost, in thousands of dollars, of airing x television commercials during a sports event is given by:

C (x) = 150 + 2,700x - 0.06x²

(a) Find the marginal cost function C' (x).

(b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars.

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Answers (2)
  1. 14 September, 03:57
    0
    a) Marginal Cost function C' (x) = 2700 - 0.12x

    (b) Marginal cost to approximate 5th commercial C' (4) = $2,699,520

    Explanation:

    The cost, in thousands of dollars, of airing x television commercials during a sports event is given by: C (x) = 150 + 2,700x - 0.06x²

    a) Marginal Cost function is = C' (x)

    C' (x) = d/dx (150 + 2,700x - 0.06x²)

    C' (x) = 0 + 2,700 - 0.06 (2x)

    C' (x) = 2700 - 0.12x

    (b) Marginal cost to approximate 5th commercial is C' (4).

    C' (4) = 2700 - 0.12 (4)

    C' (4) = 2700 - 0.48

    C' (4) = 2699.52

    In dollars, C' (4) = $2699.52 x 1000

    = $2,699,520
  2. 14 September, 03:57
    0
    That's the answer above
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