There are three convenience stores in Gambier. This week, Store I sold 80 loaves of bread, 40 quarts of milk, 12 jars of peanut butter, and 108 pounds of cold cuts. Store II sold 108 loaves of bread, 75 quarts of milk, 21 jars of peanut butter, and 147 pounds of cold cuts. Store III sold 50 loaves of bread, 30 quarts of milk, no peanut butter, and 50 pounds of cold cuts.

Complete parts (a) through (c) below.

(a) Use a [tex]$3 \times 4$[/tex] matrix to express the sales information for the three stores. Select the correct answer below.

A. [tex]$\left[\begin{array}{rrrr}80 & 12 & 108 & 40 \\ 108 & 75 & 147 & 21 \\ 50 & 0 & 50 & 30\end{array}\right]$[/tex]

B. [tex]$\left[\begin{array}{rrrr}40 & 12 & 80 & 108 \\ 108 & 21 & 147 & 75 \\ 50 & 0 & 30 & 50\end{array}\right]$[/tex]

C. [tex]$\left[\begin{array}{rrrr}80 & 40 & 12 & 108 \\ 108 & 75 & 21 & 147 \\ 50 & 30 & 0 & 50\end{array}\right]$[/tex]

D. [tex]$\left[\begin{array}{rrrr}40 & 12 & 108 & 80 \\ 21 & 108 & 147 & 75 \\ 50 & 0 & 50 & 30\end{array}\right]$[/tex]

To express the sales information for the three stores in a [tex]$3 \times 4$[/tex] matrix, we need to organize the data based on the items each store sold. The matrix is structured such that each row represents a different store and each column represents a different product category: loaves of bread, quarts of milk, jars of peanut butter, and pounds of cold cuts.

Step-by-step solution:

1. Store I Sales Data:
- Loaves of bread: 80
- Quarts of milk: 40
- Jars of peanut butter: 12
- Pounds of cold cuts: 108

Therefore, the row for Store I is [tex]$ [80, 40, 12, 108] $[/tex].

2. Store II Sales Data:
- Loaves of bread: 108
- Quarts of milk: 75
- Jars of peanut butter: 21
- Pounds of cold cuts: 147

Therefore, the row for Store II is [tex]$ [108, 75, 21, 147] $[/tex].

3. Store III Sales Data:
- Loaves of bread: 50
- Quarts of milk: 30
- Jars of peanut butter: 0
- Pounds of cold cuts: 50

Therefore, the row for Store III is [tex]$ [50, 30, 0, 50] $[/tex].

Putting these rows together, we form the [tex]$3 \times 4$[/tex] matrix as follows:

[tex]\[
\left[\begin{array}{rrrr}
80 & 40 & 12 & 108 \\
108 & 75 & 21 & 147 \\
50 & 30 & 0 & 50
\end{array}\right]
\][/tex]

Therefore, the correct answer is option C:

[tex]\[
\left[\begin{array}{rrrr}
80 & 40 & 12 & 108 \\
108 & 75 & 21 & 147 \\
50 & 30 & 0 & 50
\end{array}\right]
\][/tex]