Course Catalogue

Module Code and Title:      BMS101 Business Mathematics

Programme:                                      Bachelor of Commerce

Credit Value:                                     12

Module Tutors:                                 Hari Kumar, Jigme Tashi, Ritu Barna Adhikari

Module Coordinator:                        Jigme Tashi

General Objective: The objective of the module is to introduce students to basic quantitative tools and techniques that can be used to solve managerial and organizational problems. Students will be able to translate a verbal business problem into a mathematical model and find rational approaches of solving it. Apart from the topics in management science, students are also introduced to financial math and use of spreadsheets to solve business related problems.

Learning Outcomes – On completion of the module, students should be able to:

  1. Solve loan amortization and finance related problems with the financial functions in spreadsheets
  2. Measure input variable in business problem for a known output by using “what if analysis” function in spreadsheets
  3. Demonstrate various methods of representing large quantities of data in matrix and other forms, emphasizing the use of spreadsheets and other mathematical tools
  4. Set up and solve applied business and economic problems using a system of linear equations
  5. Select an appropriate technique of operation research in decision making relating to administrative, business and operational problems
  6. Formulate various real-life business problems mathematically using linear programming techniques
  7. Design mathematical models to solve linear programming problems by graphical method and simplex method using spreadsheets
  8. Formulate a variety of business problems into mathematical models and solve for optimization of resources and efficient functioning of an organization

Teaching and Learning Approach:

Approach

Hours per week

Total credit hours

Lecture

2

30

Class exercises & Discussion

1

15

Exercises, tests and research in computer lab

1

15

Independent study

4

60

Total

120


Assessment Approach:

A. Group Assignment / Project: Portion of Final Marks-10%

Students in groups of 4 will research any industry in Bhutan to solve a graphical or simplex linear equation with spreadsheets and write a 600-word report, plus data and graphs.

5%       primary data collection and data synthesis

5%       analysis

B. Problem Solving: Portion of Final Marks-15%

Students will individually utilize problem solving techniques taught in class to analyse two (each with 7.5%) short problems on the annuities schemes of NPPF and other schemes sold by RICBL, decide whether to buy or lease a machine using present value concept, determine the unit of production for given number of internal and external demand vectors using input-output model, or find the optimum solution for a given LPP.  The problem solving report will be 300 words.

1.5%    defining the problem mathematically

1.5%    using appropriate formula

1.5%    solving correctly

3%       correctly analyzing

C. Class tests: Portion of Final Marks-10%

Each student will individually solve application-based problems on the theoretical concepts presented in class. The written tests (5% each), one before and one after the midterm, will each take 40 minutes, and cover approximately 3-4 weeks of material.

1%       using appropriate formula

2%       solving correctly

2%       correct analysis

D. Computer Lab Tests: Portion of Final Marks-10%

Each student will complete two computer lab tests (5% each) of 30 minutes.  The first covers using spreadsheet financial functions to solve annuities and loan amortization problems, and the second covers using spreadsheets to solve systems of linear equations relating to some business problem and using spreadsheets to find the optimal solution for a linear programming problem. Grades will be given proportionately based on the percentage for each test.

1%       using appropriate formula

2%       solving correctly

2%       correct analysis

E. Midterm Examination: Portion of Final Marks-15%

Students will take a written exam of 2-hour duration covering topics up to the mid-point of the semester.

F. Semester-end Examination: Portion of Final Marks-40%

The module will have a semester-end exam for 2 hours covering the entire syllabus. The question will be divided into two parts – Part A (carrying 40% of the exam weightage) will be mostly of short answer including objective questions. Part-B (carrying almost 60% of the exam weightage) will be mostly of essay type or an extended response to the given question. This part of the question requires students to apply, analyse, and evaluate or construct knowledge and skills.

Areas of assignments

Quantity

Weight

A.    Group Assignment / Project

1

10%

B.    Problem Solving

1

15%

C.   Class tests

2

10%

D.   Computer lab tests

2

10%

E.    Midterm Examination

1

15%

Total Continuous Assessment (CA)

 

60%

F.    Semester-end Examination (SE)

 

40%

TOTAL

 

100%


Pre-requisites:None

Subject Matter:

  1. Mathematics for Finance
    • Introduction to simple and compound Interest using a case study of different options for purchasing a car.
    • Concept of interest in various business settings
    • Simple and compound interest
    • Discrete and continuous compounding
    • Compounding with changing interest rates
    • Nominal and effective rate of interest
    • Writing formula for calculating simple and compound interest in Excel
  1. Using Simple and Compound Interest to Solve Business Finance Cases
    • Considering the business situation of a car purchase, calculate compound interest in various circumstances.
    • Demonstrate the use of MS Excel function PMT and goal seek to calculate the monthly/quarterly deposits.
    • Compounding and discounting concept
    • Present and future value formula
    • Annuities: Ordinary annuity and annuity due
    • Solving annuities problem using PV, FV functions in Excel
    • Use goal seek function in Excel to solve a business problem
    • The duration of car loan installment
    • Use Excel to build a loan amortization schedule for the above situation
    • Solving business problems using financial functions in Excel (PMT, NPER, RATE)
    • Loan amortization
    • Lease versus purchase and Sinking fund
    • Making a loan amortization schedule in Excel, and testing sensitivity to changed parameters
  1. Matrix and its Application in Production Processes in Business
    • Presenting the business information in a matrix form
    • Calculating profit
    • Demonstrate use of MMULT function in Excel to solve problems
    • Introduction to matrices and determinant
    • Types of matrices, and how each type is used in business situations
    • Matrix representation of data
    • Algebra of matrices (addition, subtraction and multiplication) application in solving business problem with the help of Excel
    • Determinants, minor, co-factors and Transpose of matrix
    • Adjoint and inverse of square matrix
    • Using Excel functions SUMIF, SUMPRODUCT and MMMULT
  1. Solving Loan and Bond Issues using Linear Equations
    • Form a system of linear equation for the information given above
    • Write the coefficient matrix for above and find the determinant and inverse using MDETER and MINVERSE function in Excel
    • Find the amount of each investment using matrix algebra
    • Using a system of linear equations in solving different types of business problems
    • Matrix representation of system of equation
    • System of linear equation- business application
    • Solving system of linear equation by matrix inverse method using MINVERSE function in Excel
    • Solving system of linear equation by Cramer’s Rule using MDETERM in Excel
  1. Solving Production Problems using Technological Matrices
    • Creating the technological matrix
    • Determining gross production of both of products
    • Check the viability of the system using the Hawkins-Simon condition
    • Leontief Input-out model and its application in business and economy
    • The Leontief input-output model
    • Hawkins-Simon Conditions for the viability of the system in an economy of three sectors
  1. Linear Programming Based on Business Case Situations
    • Defining the objective
    • Defining the constraints to take into account
    • Recognizing potential restrictions
    • Solving considering system constraints
      • Formulation of Linear Programming Problem
        • General equation of LPP
        • Definition of objective function, feasible and optimum solution
        • Identification of variables, objective function and constraints
        • Formulating a word problem to LPP
      • Graphical method of solving LPP
        • Graph of linear inequality
        • Application of extreme point theorem in graphical method of solving LPP
        • Some exceptional cases in graphical method
  1. Linear Programming – The Simplex Method
    • Key questions:
      • Limitations of Graphical method be used in such kind of problems
      • An alternate way of dealing with such kind of problems
      • Helping the company in achieving their target with linear programming
      • Use of spreadsheets to solve such kind of problems
    • Introduction and some useful definition
      • Slack variable
      • Surplus variable
      • Basic solution
      • Basic feasible solution
      • A maximization case- all constraints of the type (Big-M)
    • Standard form of Simplex method and constructing Simplex tableau
    • Steps in Simplex method (maximization case)
    • Shadow price of resources
    • Breaking of Simplex method
    • Artificial variables
      • The Simplex method- A minimization case
      • Steps of the Simplex method (minimization case)
      • Identification of unique and multiple optimal solutions, unbounded solution, infeasibility and degeneracy
      • Solving of LPP by Simplex method using Excel

Reading Lists:

  1. Essential Readings
    • Thukral, J.K. (2013). Mathematics for business studies (17th ed.). Gurgoan: Scholar Tech Press.
    • Clendenen, G., & Salzman, S.A. (2014). Business mathematics (13th ed.). Pearson.
    • Sultan, A. (2014). Linear programming: An introduction with applications (2nd ed.). New York: Academic Press.
  2. Additional Readings
    • Bradley, T. (2013). Essential Mathematics for Economics and Business (4th ed.). Wiley.
    • Sharma, J.K. (2013). Operation research theory and application (5th ed.). New Delhi: Laxmi Publication.
    • Taha, H.A. (2016). Operations research: An introduction (10th ed.). Pearson.
    • Wikes, F. M. (1994). Mathematics for business, finance and economics. Thomson Business Press.

Date: July, 2017

fferentiation – increasing and decreasing functions – maxima and minima of univariate functions – concept of elasticity, elasticity of demand and supply - applied max-min problems in business and economics – concept of partial derivatives – maxima and minima of functions of two variables – complementary and competitive commodities – partial elasticities of demand – applied optimization problems in business and economics.

 

Unit-III:  Business Applications of Integral calculus                                              (10 Hours)

Concept of integration – integration techniques: substitution, integration by parts and partial fraction methods – definite integrals – applications of integration to business and economics: finding cost and revenue from the marginal functions, demand function from elasticity of demand – consumers’ and producers’ surplus.

 

Unit-IV:  Matrices and determinants                                                                         (8 Hours)

Introduction to matrices and determinants – operations on matrices – inverse of a 3 x 3 matrix – solution of system of linear equations  - application of matrices in business – Leontief input -output model.

 

Unit-V:  Probability theory                                                                                         (8 Hours)

Review of permutations and combinations – introduction to probability - addition and multiplication laws, conditional probability and Baye’s theorem.

 

Teaching Strategies

  • Lecture
  • Presentation
  • Group Assignments

 

Assessments

  • Assignments                            20%
  • Mid-semester examination      30%
  • End-semester examination      50%

 

Essential Texts

  1. Thukral, J.K. Mathematics for Business Studies, New Delhi, Mayur Publication.
  2. Mizrahi and Sullivan, Mathematics for Business and Social Sciences, John Wiley and sons.

 

References

  1. Thukral, J.K. Mathematics, 4th edition, Taxman Allied Services Pvt. Ltd.
  2. Dewling, E.T. Mathematics for Economics, McGraw Hill
  3. Lial, Greenwell and Ritchey, finite Mathematics and Calculus with applications, 6th edition, Addison Wesley Publication.
  4. Wikes, F.M. Mathematics for Business, Finance and Economics, Thomson learning.
  5. L.D. Hoffman and G.L. Bradley, Calculus for business, economics and the social and life sciences, 5th edition, McGraw Hill.
  6. Thukral, J.K. Business Statistics, Taxman Allied Services Pvt. Ltd.

 

 
Royal Thimphu College