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.
