Question

The daily production cost,
in dollars, of manufacturing t-shirts is
described by the function C (n) = n2 - 20n + 400, where
n is the number of t-shirts produced. The input-output table shows the daily product cost for manufacturing 10, 20, 30, and 50 t-shirts. Use the function to determine the cost of producing
30 and 50 t-shirts. Enter the production cost for 30 and 50 t-shirts in the input-output table below. (2 points)
n
C(n)
10
300
20
400
30

50

Answer 1

To determine the production cost for 30 and 50 t-shirts using the function \( C(n) = n^2 - 20n + 400 \), we can substitute the values of \( n \) into the function:

1. **For \( n = 30 \)**:
\[
C(30) = 30^2 - 20(30) + 400
\]
\[
C(30) = 900 - 600 + 400
\]
\[
C(30) = 700
\]

2. **For \( n = 50 \)**:
\[
C(50) = 50^2 - 20(50) + 400
\]
\[
C(50) = 2500 - 1000 + 400
\]
\[
C(50) = 1900
\]

Now, we can fill in the production costs in the input-output table:

\[
\begin{array}{|c|c|}
\hline
n & C(n) \\
\hline
10 & 300 \\
20 & 400 \\
30 & 700 \\
50 & 1900 \\
\hline
\end{array}
\]

So, the production costs are:
- For 30 t-shirts: **700 dollars**
- For 50 t-shirts: **1900 dollars**