Question

) If the average cost function for a company is given by C(x) = 0.2x + 20x −1 + 75, nd what level of production produces the lowest average cost. Additionally, nd the original cost function C(x).

Answer 1

Answer:

The correct answer is 10 for lowest average cost and the cost function is 0.2$x^{2}$ + 75x + 20.

Step-by-step explanation:

Average cost function is given by = $\frac{Cost}{Quantity}$ = C(x) = 0.2x + $\frac{20}{x}$ +75.

For minimizing we need to find $\frac{d}{dx}$C(x) = 0.

⇒ $\frac{d}{dx}$C(x) = 0.2 - $\frac{20}{x^{2}}$.

⇒ $\frac{20}{x^{2}}$ = 0.2

⇒ $x^{2}$ = 100.

⇒ x = ±10

⇒ x = 10 ; cost cannot be negative.

Second order derivative is positive which implies the average cost minimizes.

Original cost function is given by C(x) × x = 0.2$x^{2}$ + 75x + 20.