29 November, 03:01

# 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. 29 November, 04:52
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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.