Let's solve the problem step by step.
The average cost function is given by:
[tex]\[
\bar{C}(x) = \frac{1875}{x} + 50
\][/tex]
### Part 3 of 4:
We need to fill in the table for different values of [tex]\( x \)[/tex] (in thousand pages) using the average cost function [tex]\(\bar{C}(x)\)[/tex].
Given values of [tex]\( x \)[/tex] are 20, 50, 100, and 200.
1. For [tex]\( x = 20 \)[/tex]:
[tex]\[
\bar{C}(20) = \frac{1875}{20} + 50
\][/tex]
Calculate [tex]\(\frac{1875}{20}\)[/tex]:
[tex]\[
\frac{1875}{20} = 93.75
\][/tex]
Then:
[tex]\[
\bar{C}(20) = 93.75 + 50 = 143.75
\][/tex]
2. For [tex]\( x = 50 \)[/tex]:
[tex]\[
\bar{C}(50) = \frac{1875}{50} + 50
\][/tex]
Calculate [tex]\(\frac{1875}{50}\)[/tex]:
[tex]\[
\frac{1875}{50} = 37.5
\][/tex]
Then:
[tex]\[
\bar{C}(50) = 37.5 + 50 = 87.5
\][/tex]
3. For [tex]\( x = 100 \)[/tex]:
[tex]\[
\bar{C}(100) = \frac{1875}{100} + 50
\][/tex]
Calculate [tex]\(\frac{1875}{100}\)[/tex]:
[tex]\[
\frac{1875}{100} = 18.75
\][/tex]
Then:
[tex]\[
\bar{C}(100) = 18.75 + 50 = 68.75
\][/tex]
4. For [tex]\( x = 200 \)[/tex]:
[tex]\[
\bar{C}(200) = \frac{1875}{200} + 50
\][/tex]
Calculate [tex]\(\frac{1875}{200}\)[/tex]:
[tex]\[
\frac{1875}{200} = 9.375
\][/tex]
Then:
[tex]\[
\bar{C}(200) = 9.375 + 50 = 59.38
\][/tex]
Now, we can fill in the table as follows:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 20 & 50 & 100 & 200 \\
\hline
\bar{C}(x) & 143.75 & 87.5 & 68.75 & 59.38 \\
\hline
\end{array}
\][/tex]
So the table with completed values is:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 20 & 50 & 100 & 200 \\
\hline
\bar{C}(x) & 143.75 & 87.5 & 68.75 & 59.38 \\
\hline
\end{array}
\][/tex]
