Business Mathematics

802 Pages·2015·13.078 MB·English

by  P. Mariappan

I compliment Dr P. Mariappan for writing a book on Business Mathematics which covers everything
right from the basics to advance level mathematics to solve day-to-day business problems. I am sure that
this book will create a solid foundation of mathematics for the present day students and future business
leaders.
Dr Rajiv Aserkar
SK Jain School of Management, Dubai
This book is really a comprehensive covering all the aspects of theoretical and application sides of busi-
ness. The structure is designed in such a way which could explore many vital issues empathetically from
students’ point of view at the same time covering all the recent trends in business.
This book is simply superb and unique as it covers mathematics, statistics, operations research and
financial areas of business. I am confident that students can have this single book to replace three to four
different titles.
Dr A. Dunstan Rajkumar, Associate Professor
School of Social Sciences and Languages, VIT University, Tamil Nadu
This book reflects more than two decades of author involvement with business math education. It offers
perfect coverage of practical business applications of math through step-by-step evolution of concepts
and explanation, for example: numerous practice exercises, devised in a legitimate format. Business
Mathematics by Dr P. Mariappan is an excellent selection of resources to help students with all their
business math needs from the beginner to advanced level users.
Dr M. Uma Selvi, Head of Faculty of Business Management
Majan University College, Muscat, Oman
I am happy to go through the book Business Mathematics. All the fundamentals required for business
decision making are written and explained in a very simple and lucid style in order to have a thorough
understanding of the subject.
Also the presentation of the basic concept of the subject emphasis more opportunities for students to
build mathematical skills.
Dr V. Mohan, Professor and Head Department of Mathematics, Dean (P&A)
Thiagarajar College of Engineering, Madurai
Business Mathematics written by Dr Mariappan and published by Pearson covers all the concepts
which are necessary for students those who are studying Business Mathematics subject as a course. The
mathematical models and the relevant methodologies are well explained in the book. This book will be a
resource for the beginners especially for students those do not have mathematics background. I am sure
students will understand the concepts of the use of mathematics in business studies through this book. At
the outset, it is a very good book for both teaching and student community.
Dr Bhaba Krishna Mohanty, Professor
Indian Institute of Management Lucknow
Business Mathematics authored by Dr Mariappan contains all the concepts which are necessary for stu-
dents of Business Mathematics course. I am pleased to notice that the author explains all the methodolo-
gies for various mathematical models using flow-charting technique. This will help both the mathematics
and the non-mathematics students to learn the concepts very well.
M. Sambandham, Professor of Mathematics
Morehouse College Academics, Georgia, United States of America
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Business Mathematics
P. Mariappan
Associate professor
Department of Mathematics
Bishop heber College, Tiruchirappalli, Tamil Nadu
Delhi • Chennai
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Copyright © 2015 Pearson India Education Services Pvt. Ltd
Published by Pearson India Education Services Pvt. Ltd, CIN: U72200TN2005PTC057128, formerly
known as TutorVista Global Pvt. Ltd, licensee of Pearson Education in South Asia.
No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s
prior written consent.
This eBook may or may not include all assets that were part of the print version. The publisher
reserves the right to remove any material in this eBook at any time.
ISBN 978-93-325-3634-0
eISBN 978-93-325-4470-3
Head Office: A-8 (A), 7th Floor, Knowledge Boulevard, Sector 62, Noida 201 309, Uttar Pradesh,
India.
Registered Office: Module G4, Ground Floor, Elnet Software City, TS-140, Block 2 & 9, Rajiv
Gandhi Salai, Taramani, Chennai 600 113, Tamil Nadu, India.
Fax: [phone], Phone: [phone]
www.pearson.co.in, Email: [email protected]
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Brief Contents
Foreword xix
Preface xxi
Acknowledgement xxii
About the Author xxiii
Chapter 1 Introduction to Business Mathematics 1
Chapter 2 Algebra 10
Chapter 3 Theory of Sets and Its Business Applications 35
Chapter 4 Ratio 55
Chapter 5 Functions and Graphs 96
Chapter 6 Quadratic Functions and Theory of Quadratic Equations 113
Chapter 7 Permutation and Combination 136
Chapter 8 Mathematical Induction and Binomial Theorem 153
Chapter 9 Sequence and Series–Its Application to Business 166
Chapter 10 Compound Interest and Annuities 193
Chapter 11 Coordinate Geometry 211
Chapter 12 Locus and Equation to a Locus 227
Chapter 13 Straight Line 231
Chapter 14 Circle 259
Chapter 15 Matrix and Its Applications to Business 280
Chapter 16 Application of Matrix Concept 350
Chapter 17 Differential Calculus and Its Business Applications 363
Chapter 18 Applications of Integral Calculus to Business 432
Chapter 19 Functions and Their Applications to Business 470
Chapter 20 Linear Programming and Its Application to Business 479
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vi | Brief Contents
Chapter 21 Transportation Problem 560
Chapter 22 Probability Theory 685
Chapter 23 Correlation and Regression Analysis 733
Chapter 24 Concept of Shares 767
Index 771
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Contents
Foreword xix
Preface xxi
Acknowledgement xxii
About the Author xxiii
Chapter 1 Introduction to Business Mathematics 1
1.1 Introduction to Business Mathematics 1
1.2 Scope and Importance 1
1.2.1 Steps in Quantitative Analysis Approach 1
1.3 Number System 4
1.3.1 Natural Numbers 5
1.3.2 Whole Numbers 5
1.4 Positive and Negative Integers 5
1.4.1 Positive Integers 5
1.4.2 Negative Integers 5
1.5 Fractions 5
1.5.1 Proper Fraction 6
1.5.2 Improper Fraction 6
1.6 Rational and Irrational Numbers 6
1.6.1 Rational Numbers 6
1.6.2 Irrational Numbers 7
1.7 Real Numbers 7
1.8 Sum of First n Natural Numbers 7
1.9 S um of Square and Sum of Cube of First n Natural Numbers 8
Chapter 2 Algebra 10
2.1 Algebra 10
2.2 Algebraic Identities 10
2.3 Simple Factorizations 11
2.4 Equations 11
2.5 Linear and Quadratic Equations 12
2.5.1 Linear Equations 12
2.5.2 Simultaneous Linear Equations 12
2.5.3 Quadratic Equation 12
2.6 Indices and Surds 12
2.6.1 Indices 12
2.6.2 Surds 18
2.7 Logarithms and Their Properties 22
2.7.1 Definition 22
2.7.2 Properties 23
2.7.3 Common Logarithms 24
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viii | Contents
2.8 Problems Based on Logarithms 26
2.9 Inequality in Graphs 27
2.10 Remainder Theorem and Factor Theorem 29
2.10.1 Remainder Theorem 29
2.10.2 Factor Theorem 30
Exercise 30
Chapter 3 Theory of Sets and Its Business Applications 35
3.1 Set Theory 35
3.2 Representation of Sets 35
3.2.1 Tabulation Method 35
3.2.2 Set Builder Form 35
3.2.3 Cardinal Number 36
3.2.4 Element of a Set 36
3.2.5 Order of a Set 36
3.2.6 Finite Set 36
3.2.7 Infinite Set 36
3.2.8 Singleton Set 36
3.3 Union of Sets 37
3.4 Intersection of Two Sets 37
3.5 Complement of a Set 37
3.6 Subset 37
3.6.1 Identical/Equal Set 38
3.6.2 Equivalent Set 38
3.6.3 Disjoint Set 38
3.6.4 Universal Set 38
3.7 Null Set/Empty Set/Void Set 39
3.8 Difference of a Set 39
3.9 De Morgan’s Law 39
3.10 Universal Set 39
3.11 Basic Operations on Set 40
3.11.1 Union of Sets 40
3.11.2 Intersection of Two Sets 41
3.11.3 Difference of a Set 41
3.11.4 Complement of a Set 41
3.12 Cartesian Products 41
3.13 Laws of Set Algebra 42
3.14 Cardinal Numbers 42
3.15 Venn Diagram 42
3.16 Business Applications 43
Exercise 52
Chapter 4 Ratio 55
4.1 Ratio 55
4.2 Proportion 57
4.3 Types of Proportion 65
4.3.1 Direct Proportion 65
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Contents | ix
4.3.2 Inverse Proportion 65
4.3.3 Indirect Proportion 66
4.4 Ratio, Proportion and Its Type of Comparison 66
4.4.1 Addition and Subtraction of Ratios 66
4.5 Variations 68
4.5.1 Direct Variation 68
4.5.2 Inverse Variation 69
4.5.3 Joint Variation 69
4.6 Percentage 69
4.6.1 Uses of Percentages 70
4.6.2 Converting Fractions into Percentage 70
4.6.3 Problem Based on Quantity Application 71
4.6.4 Problem Based on Election Application 71
4.6.5 Problem Based on Examination Application 73
4.6.6 Price Mixture 73
4.6.7 Decimal Fraction 75
4.7 Annexing Zeros and Removing Decimal Signs 75
4.7.1 Annexing Zeros 75
4.8 Average (Arithmetic Mean) 77
4.8.1 Discrete Data 77
4.8.2 Discrete Data with Frequency 77
4.9 Computation of Mean for Grouped Series 80
4.10 Mean of Composite Group 84
Exercise 86
Chapter 5 Functions and Graphs 96
5.1 Introduction 96
5.2 Function 96
5.2.1 Constant 96
5.2.2 Variable 96
5.3 Domain and Range of a Function 97
5.4 Continuous and Discrete Functions 98
5.4.1 Continuous Function 98
5.4.2 Discrete Function 98
5.5 Composition and Inverse Functions 98
5.5.1 Composition Functions 98
5.5.2 Order of Composition 99
5.5.3 Decomposition of a Function 99
5.5.4 Inverse Function 99
5.6 Classification of Functions 100
5.7 Exponential and Logarithmic Functions 102
5.7.1 Exponential Functions 102
5.7.2 Logarithmic Functions 102
5.8 Graphs 103
5.8.1 The General Idea of Curve Sketching and Graphs of Straight Lines 103
5.9 Modulus Function 107
Exercise 108
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