The sales of certain products in three cities are given in the 4 by 3 matrix below. City 2 City 3 City 1 73 Tablets 61 Laptop Computers 76 37 Cell Phones 40 35 Personal DVR 47 52 32 The cost of the items depend if they were sold "Retail" or "Wholesale". The Retail costs were: $192 for tablets, $396 for laptops, $375 for cell phones, and $1,883 for DVRs. The Wholesale costs were: $319 for tablets, $478 for laptops, $245 for cell phones, and $1,883 for DVRs. To get the total revenue at each city for Retail and Wholesale, we would need to information above (on retail and wholesale costs) into a matrix that has rows and columns and multiply it by the 4 by 3 matrix on sales at each city for each item. After multiplying these two matrices, we would have a matrix that has rows and columns. The total wholesale revenue from city 2 would be in row column 48 44 78
The sales of certain products in three cities are given in the 4 by 3 matrix below. City 2 City 3 City 1 73 Tablets 61 Laptop Computers 76 37 Cell Phones 40 35 Personal DVR 47 52 32 The cost of the items depend if they were sold "Retail" or "Wholesale". The Retail costs were: $192 for tablets, $396 for laptops, $375 for cell phones, and $1,883 for DVRs. The Wholesale costs were: $319 for tablets, $478 for laptops, $245 for cell phones, and $1,883 for DVRs. To get the total revenue at each city for Retail and Wholesale, we would need to information above (on retail and wholesale costs) into a matrix that has rows and columns and multiply it by the 4 by 3 matrix on sales at each city for each item. After multiplying these two matrices, we would have a matrix that has rows and columns. The total wholesale revenue from city 2 would be in row column 48 44 78
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:### Understanding Sales Data through Matrix Operations
The following matrix provides the sales of certain products in three cities. The matrix is a \(4 \times 3\) matrix where rows represent different products and columns represent different cities.
#### Sales Data Matrix
| | City 1 | City 2 | City 3 |
|-------------|--------|--------|--------|
| **Tablets** | 73 | 61 | 48 |
| **Laptop Computers**| 76 | 37 | 44 |
| **Cell Phones** | 40 | 35 | 78 |
| **Personal DVR** | 47 | 52 | 32 |
The cost of the items varies depending on whether they are sold "Retail" or "Wholesale".
#### Retail Costs
- **Tablets:** \$192
- **Laptop Computers:** \$396
- **Cell Phones:** \$375
- **Personal DVR:** \$1,883
#### Wholesale Costs
- **Tablets:** \$319
- **Laptop Computers:** \$478
- **Cell Phones:** \$245
- **Personal DVR:** \$1,883
To compute the total revenue in each city for both Retail and Wholesale, follow these steps:
1. **Construct a Matrix for Costs:**
- The new matrix should include retail and wholesale costs. This matrix will have:
- **4 rows** (one for each product)
- **2 columns** (one for retail and one for wholesale)
2. **Matrix Multiplication:**
- Multiply the \(4 \times 3\) sales matrix by the \(4 \times 2\) cost matrix.
3. **Resultant Matrix:**
- The resulting matrix after the multiplication will have:
- **3 rows** (corresponding to each city)
- **2 columns** (corresponding to retail and wholesale revenues)
4. **Specific Calculation:**
- Identify the total wholesale revenue from City 2, which will be located in **row 2** and **column 2** of the resultant matrix.
In this educational demonstration, matrix operations such as multiplication help in determining revenues from different sales data efficiently and effectively. These calculations can be essential for businesses in making informed financial decisions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
