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

Question

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.
(5, 205)
(10, 220)
(20, )
(45, )

Enter the correct numbers in the 2 blank spots.

Answer 1

To determine the production cost for manufacturing 20 and 45 office chairs using the provided function \( C(n) = n^2 - 12n + 240 \), we'll substitute \( n \) with 20 and 45 respectively.

First, for 20 office chairs (\( n = 20 \)): \[ C(20) = 20^2 - 12 \cdot 20 + 240 \] Calculating this step by step: \[ = 400 - 240 + 240 \] \[ = 400 \]

So, the cost of producing 20 office chairs is 400.

Next, for 45 office chairs (\( n = 45 \)): \[ C(45) = 45^2 - 12 \cdot 45 + 240 \] Calculating this step by step: \[ = 2025 - 540 + 240 \] \[ = 2025 - 300 \] \[ = 1725 \]

So, the cost of producing 45 office chairs is 1725.

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

(5, 205)
(10, 220)
(20, 400)
(45, 1725)

So the completed table is: (5, 205)
(10, 220)
(20, 400)
(45, 1725)