A restaurant has a main location and a traveling food truck. The first matrix A shows the number of managers and associates employed. The second matrix B shows the average annual cost of salary and benefits (in thousands of dollars). Complete parts (a) through (c) below. Salary Benefits Managers 42 6 Associates 18 Restaurant Food Truck Managers Associates 6 25 2 (a) Find the matrix product AB. AB= (Simplify your answer.) 3 A B (b) Explain what AB represents. Choose the correct answer below. O A. Row 1 of AB represents the restaurant and row 2 represents the food truck. Column 1 of AB represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees. OB. Row 1 of AB represents the food truck and row 2 represents the restaurant. Column 1 of AB represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees. OC. Row 1 of AB represents the food truck and row 2 represents the restaurant. Column 1 of AB represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees. D. Row 1 of AB represents the restaurant and row 2 represents the food truck. Column 1 of AB represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees.
A restaurant has a main location and a traveling food truck. The first matrix A shows the number of managers and associates employed. The second matrix B shows the average annual cost of salary and benefits (in thousands of dollars). Complete parts (a) through (c) below. Salary Benefits Managers 42 6 Associates 18 Restaurant Food Truck Managers Associates 6 25 2 (a) Find the matrix product AB. AB= (Simplify your answer.) 3 A B (b) Explain what AB represents. Choose the correct answer below. O A. Row 1 of AB represents the restaurant and row 2 represents the food truck. Column 1 of AB represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees. OB. Row 1 of AB represents the food truck and row 2 represents the restaurant. Column 1 of AB represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees. OC. Row 1 of AB represents the food truck and row 2 represents the restaurant. Column 1 of AB represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees. D. Row 1 of AB represents the restaurant and row 2 represents the food truck. Column 1 of AB represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Understanding Matrix Multiplication in Business Operations**
A restaurant operates both a main location and a traveling food truck. The matrix operations below help in understanding their staff employment and cost management.
**Matrix A** represents the number of managers and associates employed at each location:
- \[
\text{Matrix A} = \begin{bmatrix}
6 & 25 \\
2 & 3
\end{bmatrix}
\]
- **Row 1 (Restaurant)**: 6 Managers, 25 Associates
- **Row 2 (Food Truck)**: 2 Managers, 3 Associates
**Matrix B** indicates the average annual cost in thousands of dollars for salary and benefits for managers and associates:
- \[
\text{Matrix B} = \begin{bmatrix}
42 & 6 \\
18 & 3
\end{bmatrix}
\]
- **Column 1 (Salary in $000s)**: $42,000 per Manager, $18,000 per Associate
- **Column 2 (Benefits in $000s)**: $6,000 per Manager, $3,000 per Associate
**Task (a):** Calculate the matrix product \( AB \).
\[
AB = \begin{bmatrix}
6 & 25 \\
2 & 3
\end{bmatrix}
\begin{bmatrix}
42 & 6 \\
18 & 3
\end{bmatrix}
\]
(Simplify your answer.)
**Task (b):** Interpret the meaning of the matrix \( AB \). Choose the correct explanation:
A. Row 1 of \( AB \) represents the restaurant, and row 2 represents the food truck. Column 1 of \( AB \) represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees.
B. Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees.
C. Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees.
D. Row 1 of \( AB \) represents the restaurant, and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F917d2425-81cd-4e01-b117-3301ec41a936%2F2ae66088-5a55-4cee-a38c-c92d3443f191%2Foq6tpx2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Matrix Multiplication in Business Operations**
A restaurant operates both a main location and a traveling food truck. The matrix operations below help in understanding their staff employment and cost management.
**Matrix A** represents the number of managers and associates employed at each location:
- \[
\text{Matrix A} = \begin{bmatrix}
6 & 25 \\
2 & 3
\end{bmatrix}
\]
- **Row 1 (Restaurant)**: 6 Managers, 25 Associates
- **Row 2 (Food Truck)**: 2 Managers, 3 Associates
**Matrix B** indicates the average annual cost in thousands of dollars for salary and benefits for managers and associates:
- \[
\text{Matrix B} = \begin{bmatrix}
42 & 6 \\
18 & 3
\end{bmatrix}
\]
- **Column 1 (Salary in $000s)**: $42,000 per Manager, $18,000 per Associate
- **Column 2 (Benefits in $000s)**: $6,000 per Manager, $3,000 per Associate
**Task (a):** Calculate the matrix product \( AB \).
\[
AB = \begin{bmatrix}
6 & 25 \\
2 & 3
\end{bmatrix}
\begin{bmatrix}
42 & 6 \\
18 & 3
\end{bmatrix}
\]
(Simplify your answer.)
**Task (b):** Interpret the meaning of the matrix \( AB \). Choose the correct explanation:
A. Row 1 of \( AB \) represents the restaurant, and row 2 represents the food truck. Column 1 of \( AB \) represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees.
B. Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees.
C. Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees.
D. Row 1 of \( AB \) represents the restaurant, and
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![A restaurant has a main location and a traveling food truck. The first matrix \( A \) shows the number of managers and associates employed. The second matrix \( B \) shows the average annual cost of salary and benefits (in thousands of dollars). Complete parts (a) through (c) below.
\[
\text{Restaurant}
\begin{bmatrix}
6 & 25 \\
2 & 3
\end{bmatrix}
= A
\quad \text{Managers}
\begin{bmatrix}
42 & 6 \\
18 & 3
\end{bmatrix}
= B
\quad \text{Associates}
\]
\[
\text{Salary} \quad \text{Benefits}
\]
- **B.** Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees.
- **C.** Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees.
- **D.** Row 1 of \( AB \) represents the restaurant, and row 2 represents the food truck. Column 1 of \( AB \) represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees. (Correct choice)
**(c)** According to matrix \( AB \), what is the total cost of salaries for all employees (managers and associates) at the restaurant? What is the total cost of benefits for all employees at the food truck?
- The total cost of salaries for all employees at the restaurant is \$\_\_\_\_.
- The total cost of benefits for all employees at the food truck is \$\_\_\_\_.](https://content.bartleby.com/qna-images/question/917d2425-81cd-4e01-b117-3301ec41a936/fef06039-1cf4-44b6-aa91-1106ce9b4cce/uhoba47_processed.jpeg)
Transcribed Image Text:A restaurant has a main location and a traveling food truck. The first matrix \( A \) shows the number of managers and associates employed. The second matrix \( B \) shows the average annual cost of salary and benefits (in thousands of dollars). Complete parts (a) through (c) below.
\[
\text{Restaurant}
\begin{bmatrix}
6 & 25 \\
2 & 3
\end{bmatrix}
= A
\quad \text{Managers}
\begin{bmatrix}
42 & 6 \\
18 & 3
\end{bmatrix}
= B
\quad \text{Associates}
\]
\[
\text{Salary} \quad \text{Benefits}
\]
- **B.** Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees.
- **C.** Row 1 of \( AB \) represents the food truck, and row 2 represents the restaurant. Column 1 of \( AB \) represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees.
- **D.** Row 1 of \( AB \) represents the restaurant, and row 2 represents the food truck. Column 1 of \( AB \) represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees. (Correct choice)
**(c)** According to matrix \( AB \), what is the total cost of salaries for all employees (managers and associates) at the restaurant? What is the total cost of benefits for all employees at the food truck?
- The total cost of salaries for all employees at the restaurant is \$\_\_\_\_.
- The total cost of benefits for all employees at the food truck is \$\_\_\_\_.
Solution
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