There are three convenience stores in Gambier. This week, Store I sold 84 loaves of bread, 48 quarts of milk, 12 jars of peanut butter, and 108 pounds of cold cuts. Store II sold 105 loaves of bread, 69 quarts of milk, 18 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 70 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]$\left[\begin{array}{rrrr}48 & 12 & 108 & 84 \\ 18 & 105 & 147 & 69 \\ 70 & 0 & 50 & 30\end{array}\right]$[/tex]

B. [tex]$\left[\begin{array}{rrrr}84 & 12 & 108 & 48 \\ 105 & 69 & 147 & 18 \\ 50 & 0 & 70 & 30\end{array}\right]$[/tex]

C. [tex]$\left[\begin{array}{rrrr}48 & 12 & 84 & 108 \\ 105 & 18 & 147 & 69 \\ 50 & 0 & 30 & 70\end{array}\right]$[/tex]

D. [tex]$\left[\begin{array}{rrrr}84 & 48 & 12 & 108 \\ 105 & 69 & 18 & 147 \\ 50 & 30 & 0 & 70\end{array}\right]$[/tex]

Sure! Let's organize the sales information for the three stores into a matrix. The matrix will have 3 rows and 4 columns, where each row represents a store, and each column represents a product category (loaves of bread, quarts of milk, jars of peanut butter, and pounds of cold cuts).

Here's how we can structure the matrix:

1. Store I sales:
- 84 loaves of bread
- 48 quarts of milk
- 12 jars of peanut butter
- 108 pounds of cold cuts

2. Store II sales:
- 105 loaves of bread
- 69 quarts of milk
- 18 jars of peanut butter
- 147 pounds of cold cuts

3. Store III sales:
- 50 loaves of bread
- 30 quarts of milk
- 0 jars of peanut butter
- 70 pounds of cold cuts

Now, placing these sales into a [tex]$3 \times 4$[/tex] matrix, where each row represents one store, we get:

[tex]\[
\begin{bmatrix}
84 & 48 & 12 & 108 \\
105 & 69 & 18 & 147 \\
50 & 30 & 0 & 70
\end{bmatrix}
\][/tex]

So, the matrix that corresponds to the given sales data is:

[tex]\[
D.
\begin{bmatrix}
84 & 48 & 12 & 108 \\
105 & 69 & 18 & 147 \\
50 & 30 & 0 & 70
\end{bmatrix}
\][/tex]

This matrix correctly represents the sales information for the three stores.