) 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).

The correct answer is 10 for lowest average cost and the cost function is 0.2 + 75x + 20.

Step-by-step explanation:

Average cost function is given by = = C(x) = 0.2x + +75.

For minimizing we need to find C(x) = 0.

⇒ C(x) = 0.2 - .

⇒ = 0.2

⇒ = 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 + 75x + 20.