3.1 Matrices are fundamental data structures used in various computing applications for organizing and processing data efficiently. Work with the given dataset and demonstrate the use of matrices to represent the ordered data. Dataset: Consider a dataset containing the monthly sales and expenses of a small business over a year. This dataset consists of 12 months, and each month's sales revenue and expenses are recorded. Month Sales ($ thousands) Expenses ($ thousands) January 50 30 February 55 35 March 60 40 April 70 45 May 80 50 June 90 55 July 100 60 August 110 65 September 120 70 October 130 75 November 140 80 December 150 85 i) Create a matrix M to represent this dataset, where each row represents a month, and each column represents a specific attribute (e.g., month number, total sales, profit, expenses, etc.). Populate the matrix M with the relevant data from the dataset. Perform matrix operations on M to: ii) 111) a) calculate the Total Sales for each quarter. b) calculate the Monthly Variations To calculate the monthly variations in profit, you may subtract the profit for each month from the profit of the previous month. The result is a matrix showing the change in profit from one month to the next. c) calculate the total annual profit To calculate the total annual profit, you may sum the monthly profit values using matrix multiplication. This operation calculates the dot product of the monthly profit matrix and a matrix of ones to obtain the total annual profit.
3.1 Matrices are fundamental data structures used in various computing applications for organizing and processing data efficiently. Work with the given dataset and demonstrate the use of matrices to represent the ordered data. Dataset: Consider a dataset containing the monthly sales and expenses of a small business over a year. This dataset consists of 12 months, and each month's sales revenue and expenses are recorded. Month Sales ($ thousands) Expenses ($ thousands) January 50 30 February 55 35 March 60 40 April 70 45 May 80 50 June 90 55 July 100 60 August 110 65 September 120 70 October 130 75 November 140 80 December 150 85 i) Create a matrix M to represent this dataset, where each row represents a month, and each column represents a specific attribute (e.g., month number, total sales, profit, expenses, etc.). Populate the matrix M with the relevant data from the dataset. Perform matrix operations on M to: ii) 111) a) calculate the Total Sales for each quarter. b) calculate the Monthly Variations To calculate the monthly variations in profit, you may subtract the profit for each month from the profit of the previous month. The result is a matrix showing the change in profit from one month to the next. c) calculate the total annual profit To calculate the total annual profit, you may sum the monthly profit values using matrix multiplication. This operation calculates the dot product of the monthly profit matrix and a matrix of ones to obtain the total annual profit.
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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Transcribed Image Text:3.1
Matrices are fundamental data structures used in various computing applications for
organizing and processing data efficiently.
Work with the given dataset and demonstrate the use of matrices to represent the ordered
data.
Dataset:
Consider a dataset containing the monthly sales and expenses of a small business over a year.
This dataset consists of 12 months, and each month's sales revenue and expenses are
recorded.
Month
Sales ($ thousands)
Expenses ($ thousands)
January
50
30
February
55
35
March
60
40
April
70
45
May
80
50
June
90
55
July
100
60
August
110
65
September
120
70
October
130
75
November
140
80
December
150
85
i)
Create a matrix M to represent this dataset, where each row represents a month, and
each column represents a specific attribute (e.g., month number, total sales, profit,
expenses, etc.).
Populate the matrix M with the relevant data from the dataset.
Perform matrix operations on M to:
ii)
111)
a) calculate the Total Sales for each quarter.
b) calculate the Monthly Variations
To calculate the monthly variations in profit, you may subtract the profit for each
month from the profit of the previous month. The result is a matrix showing the
change in profit from one month to the next.
c) calculate the total annual profit
To calculate the total annual profit, you may sum the monthly profit values using
matrix multiplication. This operation calculates the dot product of the monthly
profit matrix and a matrix of ones to obtain the total annual profit.
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