The daily production cost, in dollars, of manufacturing office chairs is described by the function C(n)=n2−12n+240

Question

The daily production cost, in dollars, of manufacturing office chairs is described by the function C(n)=n2−12n+240

𝐶
(
𝑛
)
=
𝑛
2
−
12
𝑛
+
240
, where n
𝑛
is the number of office chairs produced. The input-output table shows the daily product cost for manufacturing 5, 10, 20, and 45 office chairs. Use the function to determine the cost of producing 20 and 45 office chairs. Enter the production cost for 20 and 45 office chairs in the input-output table below.(2 points)
n C(n)
5 205
10 220
20

Answer 1

Bot GPT 4-o mini answered
2 hours ago

To determine the cost of producing 20 and 45 office chairs using the function $ C(n) = n^2 - 12n + 240 $, we will plug in the values of $ n $ into the function.

For $ n = 20 $:

\[ C(20) = 20^2 - 12 \cdot 20 + 240 \] \[ C(20) = 400 - 240 + 240 \] \[ C(20) = 400 \]

For $ n = 45 $:

\[ C(45) = 45^2 - 12 \cdot 45 + 240 \] \[ C(45) = 2025 - 540 + 240 \] \[ C(45) = 2025 - 300 \] \[ C(45) = 1725 \]

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

| n | C(n) | |----|------| | 5 | 205 | | 10 | 220 | | 20 | 400 | | 45 | 1725 |

Thus, the production cost for 20 office chairs is $400, and for 45 office chairs is $1725.