The daily production cost,

Question

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