### Manufacturing and Wages Calculation for Boat SizesA company has two factories that manufacture three sizes of boats. The number of hours of labor required to manufacture each size are represented by matrix $ S $. The wages of the workers are represented by matrix $ T $.#### Labor Hours for Manufacturing (Matrix $ S $)\[S = \begin{pmatrix} 1.0 & 0.5 & 0.2 \\ 1.6 & 1.0 & 0.2 \\ 2.5 & 2.0 & 1.4 \\\end{pmatrix}\]- **Rows**: Boat size (Small, Medium, Large)- **Columns**: Department (Cutting, Assembly, Packaging)#### Wages for Workers (Matrix $ T $)\[T = \begin{pmatrix} 15 & 18 \\ 11 & 13 \\ 12 & 11 \\\end{pmatrix}\]- **Rows**: Department (Cutting, Assembly, Packaging)- **Columns**: Factory (A, B)#### Calculate $ST$To find the cost of manufacturing each size of boat in each factory, compute the product of matrices $ S $ and $ T $:\[ST = \begin{pmatrix} 1.0 & 0.5 & 0.2 \\ 1.6 & 1.0 & 0.2 \\ 2.5 & 2.0 & 1.4 \\\end{pmatrix}\times\begin{pmatrix} 15 & 18 \\ 11 & 13 \\ 12 & 11 \\\end{pmatrix}\]#### Steps to Compute $ST$1. **Matrix Multiplication**: Each element of the resulting matrix is calculated by multiplying the elements of the rows of $ S $ with the corresponding elements of the columns of $ T $ and summing the results. For instance: - For Small boats in Factory A: \[ (1.0 \times 15) + (0.5 \times 11) + (0.2 \times 12) \] - For Small boats in Factory B:

Given, number of hours of labor required to manufacture each size of boats S and wages of worker T,…

A company has two factories that manufacture three sizes of boats. The numbers of hours of labor required to manufacture each size are represented by S. Department Cutting Assembly Packaging 1,0 0.5 Small SEN 1,6 0.2 0.2 1.0 Medium Boat size 2,5 2.0 1.4 Large The wages of the workers are represented by T. Factory B Cutting G 18 Assembly $14 Packaging) 2 K yo Department

A company has two factories that manufacture three sizes of boats. The numbers of hours of labor required to manufacture each size are represented by S. Department Cutting Assembly Packaging 1,0 0.5 Small SEN 1,6 0.2 0.2 1.0 Medium Boat size 2,5 2.0 1.4 Large The wages of the workers are represented by T. Factory B Cutting G 18 Assembly $14 Packaging) 2 K yo Department

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Manufacturing and Wages Calculation for Boat Sizes

A company has two factories that manufacture three sizes of boats. The number of hours of labor required to manufacture each size are represented by matrix $ S $. The wages of the workers are represented by matrix $ T $.

#### Labor Hours for Manufacturing (Matrix $ S $)

\[
S =
\begin{pmatrix}
1.0 & 0.5 & 0.2 \\
1.6 & 1.0 & 0.2 \\
2.5 & 2.0 & 1.4 \\
\end{pmatrix}
\]

- **Rows**: Boat size (Small, Medium, Large)
- **Columns**: Department (Cutting, Assembly, Packaging)

#### Wages for Workers (Matrix $ T $)

\[
T =
\begin{pmatrix}
15 & 18 \\
11 & 13 \\
12 & 11 \\
\end{pmatrix}
\]

- **Rows**: Department (Cutting, Assembly, Packaging)
- **Columns**: Factory (A, B)

#### Calculate $ST$

To find the cost of manufacturing each size of boat in each factory, compute the product of matrices $ S $ and $ T $:

\[
ST =
\begin{pmatrix}
1.0 & 0.5 & 0.2 \\
1.6 & 1.0 & 0.2 \\
2.5 & 2.0 & 1.4 \\
\end{pmatrix}
\times
\begin{pmatrix}
15 & 18 \\
11 & 13 \\
12 & 11 \\
\end{pmatrix}
\]

#### Steps to Compute $ST$

1. **Matrix Multiplication**: Each element of the resulting matrix is calculated by multiplying the elements of the rows of $ S $ with the corresponding elements of the columns of $ T $ and summing the results.

For instance:

- For Small boats in Factory A:
\[
(1.0 \times 15) + (0.5 \times 11) + (0.2 \times 12)
\]
- For Small boats in Factory B:

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