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Answer :
We want to create a [tex]$3 \times 4$[/tex] matrix where each row represents one store and the columns represent the following items in this order: loaves of bread, quarts of milk, jars of peanut butter, and pounds of cold cuts.
Step 1. For Store I, the sales are:
[tex]$$
\text{Bread} = 80,\quad \text{Milk} = 40,\quad \text{Peanut Butter} = 16,\quad \text{Cold Cuts} = 116.
$$[/tex]
So the first row is:
[tex]$$
[80,\ 40,\ 16,\ 116].
$$[/tex]
Step 2. For Store II, the sales are:
[tex]$$
\text{Bread} = 105,\quad \text{Milk} = 75,\quad \text{Peanut Butter} = 24,\quad \text{Cold Cuts} = 150.
$$[/tex]
So the second row is:
[tex]$$
[105,\ 75,\ 24,\ 150].
$$[/tex]
Step 3. For Store III, the sales are:
[tex]$$
\text{Bread} = 50,\quad \text{Milk} = 40,\quad \text{Peanut Butter} = 0,\quad \text{Cold Cuts} = 50.
$$[/tex]
So the third row is:
[tex]$$
[50,\ 40,\ 0,\ 50].
$$[/tex]
Step 4. Putting these rows together, we get the complete matrix:
[tex]$$
\begin{bmatrix}
80 & 40 & 16 & 116 \\
105 & 75 & 24 & 150 \\
50 & 40 & 0 & 50
\end{bmatrix}.
$$[/tex]
Step 5. Comparing with the provided options, we see that this matrix is exactly the one in Option B.
Thus, the correct answer is Option B.
Step 1. For Store I, the sales are:
[tex]$$
\text{Bread} = 80,\quad \text{Milk} = 40,\quad \text{Peanut Butter} = 16,\quad \text{Cold Cuts} = 116.
$$[/tex]
So the first row is:
[tex]$$
[80,\ 40,\ 16,\ 116].
$$[/tex]
Step 2. For Store II, the sales are:
[tex]$$
\text{Bread} = 105,\quad \text{Milk} = 75,\quad \text{Peanut Butter} = 24,\quad \text{Cold Cuts} = 150.
$$[/tex]
So the second row is:
[tex]$$
[105,\ 75,\ 24,\ 150].
$$[/tex]
Step 3. For Store III, the sales are:
[tex]$$
\text{Bread} = 50,\quad \text{Milk} = 40,\quad \text{Peanut Butter} = 0,\quad \text{Cold Cuts} = 50.
$$[/tex]
So the third row is:
[tex]$$
[50,\ 40,\ 0,\ 50].
$$[/tex]
Step 4. Putting these rows together, we get the complete matrix:
[tex]$$
\begin{bmatrix}
80 & 40 & 16 & 116 \\
105 & 75 & 24 & 150 \\
50 & 40 & 0 & 50
\end{bmatrix}.
$$[/tex]
Step 5. Comparing with the provided options, we see that this matrix is exactly the one in Option B.
Thus, the correct answer is Option B.
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