Wally's Wagons is a store that sells wagons. The store sells three sizes of wagons: small, medium, and large. Matrix A shows the number of wagons sold at two different locations during the month of June. 50 90 30 A = %3D 25 50 50 Each wagon must be assembled and then packaged. Matrix B shows the number of minutes required for assembly and packaging of the three different-sized wagons. 15 5 B = 20 8 30 12. How can these matrices be used to determine the total number of minutes spent on assembly and packaging of the wagons in June at these two stores?

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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The image contains an educational exercise on matrix multiplication. It provides a prompt that reads:

"Drag a phrase or matrix to each box to correctly complete the statements."

Below the prompt, a statement reads: "The product of these matrices would be a 2 × 2 matrix, where the rows represent the [ ], and the columns represent the [ ]. This product matrix would be [ ]."

Several boxes are present next to the statements, to be filled with appropriate phrases or matrices:

1. A section labeled "task performed" with the matrix:
   \[
   \begin{bmatrix}
   3450 & 1330 \\
   2875 & 1125 
   \end{bmatrix}
   \]

2. A section labeled "different stores" with the matrix:
   \[
   \begin{bmatrix}
   1125 & 2875 \\
   1330 & 3450 
   \end{bmatrix}
   \]

3. A section labeled "different sizes" with the matrix:
   \[
   \begin{bmatrix}
   1330 & 2875 \\
   1125 & 3450 
   \end{bmatrix}
   \]

The goal is to match matrices and phrases to correctly complete the provided statements.
Transcribed Image Text:The image contains an educational exercise on matrix multiplication. It provides a prompt that reads: "Drag a phrase or matrix to each box to correctly complete the statements." Below the prompt, a statement reads: "The product of these matrices would be a 2 × 2 matrix, where the rows represent the [ ], and the columns represent the [ ]. This product matrix would be [ ]." Several boxes are present next to the statements, to be filled with appropriate phrases or matrices: 1. A section labeled "task performed" with the matrix: \[ \begin{bmatrix} 3450 & 1330 \\ 2875 & 1125 \end{bmatrix} \] 2. A section labeled "different stores" with the matrix: \[ \begin{bmatrix} 1125 & 2875 \\ 1330 & 3450 \end{bmatrix} \] 3. A section labeled "different sizes" with the matrix: \[ \begin{bmatrix} 1330 & 2875 \\ 1125 & 3450 \end{bmatrix} \] The goal is to match matrices and phrases to correctly complete the provided statements.
**Matrix Application in Wagon Sales and Manufacturing**

Wally’s Wagons is a store that sells wagons in three sizes: small, medium, and large. 

**Matrix A** represents the number of wagons sold at two different locations during the month of June:

\[
A = \begin{bmatrix} 
50 & 90 & 30 \\ 
25 & 50 & 50 
\end{bmatrix}
\]

- The first row corresponds to the first location and lists the number of small, medium, and large wagons sold, respectively: 50 small, 90 medium, and 30 large.
- The second row corresponds to the second location and lists: 25 small, 50 medium, and 50 large.

Each wagon requires time for assembly and packaging. 

**Matrix B** represents the number of minutes required for assembly and packaging of the three different-sized wagons:

\[
B = \begin{bmatrix} 
15 & 5 \\ 
20 & 8 \\ 
30 & 12 
\end{bmatrix}
\]

- The first column in Matrix B represents assembly time in minutes for small, medium, and large wagons: 15, 20, and 30 minutes, respectively.
- The second column represents packaging time in minutes for small, medium, and large wagons: 5, 8, and 12 minutes, respectively.

**Problem Statement:**

How can these matrices be used to determine the total number of minutes spent on assembly and packaging of the wagons in June at these two stores?

To find the total time spent, you would multiply Matrix A by Matrix B. This matrix multiplication will yield a new matrix that represents the total assembly and packaging time for wagons sold at each location.
Transcribed Image Text:**Matrix Application in Wagon Sales and Manufacturing** Wally’s Wagons is a store that sells wagons in three sizes: small, medium, and large. **Matrix A** represents the number of wagons sold at two different locations during the month of June: \[ A = \begin{bmatrix} 50 & 90 & 30 \\ 25 & 50 & 50 \end{bmatrix} \] - The first row corresponds to the first location and lists the number of small, medium, and large wagons sold, respectively: 50 small, 90 medium, and 30 large. - The second row corresponds to the second location and lists: 25 small, 50 medium, and 50 large. Each wagon requires time for assembly and packaging. **Matrix B** represents the number of minutes required for assembly and packaging of the three different-sized wagons: \[ B = \begin{bmatrix} 15 & 5 \\ 20 & 8 \\ 30 & 12 \end{bmatrix} \] - The first column in Matrix B represents assembly time in minutes for small, medium, and large wagons: 15, 20, and 30 minutes, respectively. - The second column represents packaging time in minutes for small, medium, and large wagons: 5, 8, and 12 minutes, respectively. **Problem Statement:** How can these matrices be used to determine the total number of minutes spent on assembly and packaging of the wagons in June at these two stores? To find the total time spent, you would multiply Matrix A by Matrix B. This matrix multiplication will yield a new matrix that represents the total assembly and packaging time for wagons sold at each location.
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