The chart below shows the number of small and large packages of a certain brand of cereal that were bought over a three - day period. The proce of a small box of this brand is $ 2.99, and the price of a large box is $3.99. Which of the following matrix expression represents the income, in dollars, received from the sale of cereal each of the three days ?
`{:(,"Day 1","Day 2","Day 3"),("Large",75,82,57),("Small",43,36,50):}`

Options

A. `[(75,82,57),(43,36,50)][2.99" "3.99]`
B. `[(75,43),(82,36),(57,50)][(3.99),(2.99)]`
C. `[(75,82,57),(43,36,50)][(2.99),(3.99)]`
D. `[(2.99),(3.99)][(75,43),(82,36),(57,50)]`

Explanation

To solve the problem, we need to represent the income received from the sale of cereal over three days using matrix expressions. Here’s a step-by-step breakdown of how to approach this:

### Step 1: Define the matrices

1. **Matrix A**: This matrix will represent the number of packages sold. It will have two rows (for small and large packages) and three columns (for each day).
\[ A = \begin{pmatrix} 75 & 82 & 57 \\ 43 & 36 & 50 \end{pmatrix} \]

2. **Matrix B**: This matrix will represent the prices of the packages. It will have two rows (for small and large packages) and one column.
\[ B = \begin{pmatrix} 3.99 \\ 2.99 \end{pmatrix} \]

### Step 2: Set up the income calculation

The income for each day can be calculated by multiplying the number of packages sold (Matrix A) by the prices (Matrix B). The resulting matrix will represent the income for each day.

### Step 3: Perform the matrix multiplication

To find the income, we perform the multiplication \( A \times B \):
\[ \text{Income} = A \times B = \begin{pmatrix} 75 & 82 & 57 \\ 43 & 36 & 50 \end{pmatrix} \times \begin{pmatrix} 3.99 \\ 2.99 \end{pmatrix} \]

### Step 4: Calculate the income for each day

For each day, we calculate the income as follows:

- **Day 1**:
\[ \text{Income}_1 = (75 \times 3.99) + (43 \times 2.99) \]

- **Day 2**:
\[ \text{Income}_2 = (82 \times 3.99) + (36 \times 2.99) \]

- **Day 3**:
\[ \text{Income}_3 = (57 \times 3.99) + (50 \times 2.99) \]

### Step 5: Combine the results

The final income matrix will be:
\[ \text{Income} = \begin{pmatrix} \text{Income}_1 \\ \text{Income}_2 \\ \text{Income}_3 \end{pmatrix} \]

### Final Result

The resulting matrix will give us the total income for each of the three days.