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aev [14]
3 years ago
10

) 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 low

est average cost. Additionally, nd the original cost function C(x).
Mathematics
1 answer:
Stells [14]3 years ago
5 0

Answer:

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

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The most important property of g and f being inverses of each other, is that 

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