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?

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.