Questions: 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 1 24 1 5] = A Managers Associates [35 5 18 2] = B (a) Find the matrix product AB. AB= (Simplify your answer.) (b) Explain what AB represents. Choose the correct answer below. 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 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. C. Row 1 of AB represents the food truck and row 2 represents the restaurant. Column 1 of AB represents

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 1 24 1 5] = A Managers Associates [35 5 18 2] = B (a) Find the matrix product AB. AB= (Simplify your answer.) (b) Explain what AB represents. Choose the correct answer below. 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 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. C. Row 1 of AB represents the food truck and row 2 represents the restaurant. Column 1 of AB represents
Transcript 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. \[ \left[\begin{array}{cc} \text { Salary } & \text { Benefits } \\ 1 & 24 \\ 1 & 5 \end{array}\right]=\mathrm{A} \quad \begin{array}{l} \text { Managers } \\ \text { Associates } \end{array}\left[\begin{array}{cc} 35 & 5 \\ 18 & 2 \end{array}\right]=\mathrm{B} \] (a) Find the matrix product AB . $A B=$ $\square$ (Simplify your answer.) (b) Explain what AB represents. Choose the correct answer below. A. Row 1 of $A B$ represents the restaurant and row 2 represents the food truck. Column 1 of $A B$ represents total benefits (in thousands) and column 2 represents total salary (in thousands) for all employees. B. Row 1 of $A B$ represents the restaurant and row 2 represents the food truck. Column 1 of $A B$ represents total salary (in thousands) and column 2 represents total benefits (in thousands) for all employees. C. Row 1 of $A B$ represents the food truck and row 2 represents the restaurant. Column 1 of $A B$ represents
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Solution

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Solution Steps

Step 1: Calculate the Matrix Product \( AB \)

The matrix product \( AB \) is calculated as follows:

\[ AB = \left[\begin{matrix} 1 & 24 \\ 1 & 5 \end{matrix}\right] \cdot \left[\begin{matrix} 35 & 5 \\ 18 & 2 \end{matrix}\right] = \left[\begin{matrix} 467 & 53 \\ 125 & 15 \end{matrix}\right] \]

Step 2: Interpret the Result

The resulting matrix \( AB \) can be interpreted as follows:

  • Row 1 of \( AB \) represents the total salary and benefits for managers.
  • Row 2 of \( AB \) represents the total salary and benefits for associates.
  • Column 1 of \( AB \) represents total salary (in thousands) for all employees.
  • Column 2 of \( AB \) represents total benefits (in thousands) for all employees.

Final Answer

The matrix product \( AB \) is

\[ \boxed{\left[\begin{matrix} 467 & 53 \\ 125 & 15 \end{matrix}\right]} \]

The correct interpretation of \( AB \) is option B: 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.

Thus, the answer is

\[ \boxed{B} \]

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