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

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.