A company determines that its marginal​ cost, in​ dollars, for producing x units of a product is given by Upper C prime (x )equals4500 x Sup

Question

A company determines that its marginal​ cost, in​ dollars, for producing x units of a product is given by Upper C prime (x )equals4500 x Superscript negative 1.9​, where xgreater than or equals1.11. Suppose that it were possible for the company to make infinitely many units of this product. What would the total cost be?

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Isabella 1 month 2021-10-20T23:40:42+00:00 1 Answer 0 views 0

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    2021-10-20T23:41:42+00:00

    Answer:

    Total Cost = Fixed Cost as x –> ∞

    Step-by-step explanation:

    C'(x) = 4500 x⁻¹•⁹ where x ≥ 1

    Marginal Cost = C'(x) = (dC/dx)

    C(x) = ∫ (marginal cost) dx

    C(x) = ∫ (4500 x⁻¹•⁹)

    C(x) = (-5000 x⁻⁰•⁹) + k

    where k = constant of integration or in economics term, K = Fixed Cost.

    C(x) = [-5000/(x⁰•⁹)] + Fixed Cost

    The company wants to make infinitely many units, that is, x –> ∞

    C(x –> ∞) = [-5000/(∞⁰•⁹)] + Fixed Cost

    (∞⁰•⁹) = ∞

    C(x –> ∞) = [-5000/(∞)] + Fixed Cost

    But mathematically, any number divide by infinity = 0;

    (-5000/∞) = 0

    C(x –> ∞) = 0 + Fixed Cost = Fixed Cost.

    Total Cost of producing infinite number of units for this cost function is totally the Fixed Cost.

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