Mathematics, 21.10.2020 16:01 lee9724

Consider the following cost function. A. Find the average cost and marginal cost functions.
B. Determine the average and marginal cost when x = a.
C. Interpret the values obtained in part (b).
C(x) = 1000 + 0.1x, 0 ≤ x ≤ 50000 ≤ x ≤ 5000, a = 2000

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Answer from: Erinkim2292

a)Average cost function = $\bar{C(x)}=\frac{1000+0.1x}{x}$

Marginal cost function = C'x=0.1

b) $\bar{C(2000)}=0.6$

C'(2000)=0.1

c) $\bar{C(2000)}=0.6$ is the average cost to produce first 2000 items

C'(2000)=0.1 is the marginal cost to produce 2001 th item

Step-by-step explanation:

Cost function: C(x) = 1000 + 0.1x

a)Find the average cost and marginal cost functions.

Average cost function = $\bar{C(x)}=\frac{C(x)}{x}$

Average cost function = $\bar{C(x)}=\frac{1000+0.1x}{x}$

Marginal cost function = C'x=0.1

b) Determine the average and marginal cost when x = a.

a = 2000

Average cost function = $\bar{C(x)}=\frac{1000+0.1x}{x}=\frac{1000+0.1a}{a}=\frac{1000+0.1(2000)}{2000}=0.6$

So, $\bar{C(2000)}=0.6$

Marginal cost function = C'(2000)=0.1

c)Interpret the values obtained in part (b).

$\bar{C(2000)}=0.6$ is the average cost to produce first 2000 items

C'(2000)=0.1 is the marginal cost to produce 2001 th item

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step-by-step explanation:

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Consider the following cost function. A. Find the average cost and marginal cost functions.
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