Let's go through this step-by-step:
a. We need to complete the marginal cost column in the table. The marginal cost is calculated as the difference between the total cost of producing [tex]\(n\)[/tex] tie-dyed t-shirts and the total cost of producing [tex]\(n-1\)[/tex] tie-dyed t-shirts.
From the given result:
- The marginal cost for the 1st tie-dyed t-shirt is [tex]$5. \(\$[/tex]25 - \[tex]$20 = \$[/tex]5\).
- The marginal cost for the 2nd tie-dyed t-shirt is [tex]$3. \(\$[/tex]28 - \[tex]$25 = \$[/tex]3\).
- The marginal cost for the 3rd tie-dyed t-shirt is [tex]$2. \(\$[/tex]30 - \[tex]$28 = \$[/tex]2\).
- The marginal cost for the 4th tie-dyed t-shirt is [tex]$4. \(\$[/tex]34 - \[tex]$30 = \$[/tex]4\).
- The marginal cost for the 5th tie-dyed t-shirt is [tex]$5. \(\$[/tex]39 - \[tex]$34 = \$[/tex]5\).
- The marginal cost for the 6th tie-dyed t-shirt is [tex]$9. \(\$[/tex]48 - \[tex]$39 = \$[/tex]9\).
So, the completed table should look like this:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Output} & \begin{array}{c}
\text{Total Cost} \\
\text{(dollars)}
\end{array} & \begin{array}{c}
\text{Marginal Cost} \\
\text{(dollars)}
\end{array} \\
\hline
0 & \$20 & - \\
\hline
1 & 25 & \$5 \\
\hline
2 & 28 & \$3 \\
\hline
3 & 30 & \$2 \\
\hline
4 & 34 & \$4 \\
\hline
5 & 39 & \$5 \\
\hline
6 & 48 & \$9 \\
\hline
\end{array}
\][/tex]
b. What is the total cost of producing 5 tie-dyed t-shirts?
From the given result:
- The total cost of producing 5 tie-dyed t-shirts is [tex]$\$[/tex]39[tex]$.
c. What is the marginal cost of producing the 5th tie-dyed t-shirt?
From the given result:
- The marginal cost of producing the 5th tie-dyed t-shirt is $[/tex]\[tex]$5$[/tex].
So the answers are:
b. [tex]\(\$39\)[/tex]
c. [tex]\(\$5\)[/tex]
