Course Catalogue

Module Code and Title:   BMS303 Mathematics for Managerial Decisions

Programme:                          Bachelor of Commerce

Credit Value:                         12

Module Tutors:                     Hari Kumar Tiwari, Jigme Tashi, Tshering Pemo, Dr.Robert L Holliday

Module Coordinator:            Jigme Tashi

 

General objective: The module aims to strengthen the basic mathematical concepts of functions, differential and integral calculus that can be applied in various business and economic problems. The module also focuses on formulating and solving transportation and assignment problems that arise in business. The Transportation and Assignment problems are used for facility location analysis in order to minimize shipment costs. Besides, decision analysis is introduced so that students would be able to take business decisions in an environment where there are uncertainty and risk.

 

Learning outcomes – On completion of the module, students will be able to:

  1. Apply functions and its types in various business decisions,
  2. Demonstrate mathematical models using functions,
  3. Determine Break-Even Values that are necessary for business analysis,
  4. Solve business and economic problems using limits and continuity,
  5. Apply derivatives in optimization problems of business and economics,
  6. Compute indefinite and definite integrals,
  7. Set up and solve Transportation and Assignment Problems of business,
  8. Apply mathematical tools in finding a solution to a problem or make decisions under certain, uncertain and risky environments.

 

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:

  1. Project: Portion of Final Marks: 10%

Students in groups of 4 or 5 will research problems pertaining to Transportation / Assignment / Decision Analysis / Break-Even Analysis / Mathematical Modelling of Revenue, Cost and Profit functions for any industry in Bhutan.  A presentation is to be made. 

2%       Primary data collection and data synthesis

4%       Analysis

4%       Presentation

  1. Problem Solving: Portion of Final Marks: 10%

Students will individually utilize problem solving techniques taught in class using VLE.  Students need to take up customized VLE test after the completion of every unit.  All the test scores finally will be graded to 10%.

  1. Class tests: Portion of Final Marks: 10%

Each student will individually solve application-based problems on the theoretical concepts presented in class. The written test will take 40 minutes.

2%       Using Appropriate Formula

4%       Solving Correctly

4%       Correct Analysis

  1. Computer Lab Test: Portion of Final Marks: 10%

Each student will complete a computer lab test (10%) of 30 minutes.  The lab test is to assess student’s ability in applying excel while solving Transportation and Assignment Problems.  Grades will be given proportionately based on the percentage for each test.

6%       Solving Correctly

4%       Correct Analysis

  1. Midterm Examination: Portion of Final Marks: 20%

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

  1. 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.    Project

1

10%

B.    Problem Solving

2

10%

C.   Class tests

1

10%

D.   Computer lab test

1

10%

E.    Midterm Examination

1

20%

Total Continuous Assessment (CA)

 

60%

Semester-End Examination (SE)

 

40%

Pre-requisites: BMS101 Business Mathematics

Subject matter:

  1. Functions, Limits and Continuity
  • Introduction to Functions
  • Types of Functions
    • Linear Functions
    • Non-Linear Functions
  • The Graph of a Linear and Non-Linear Functions
  • Functional Models and Break Even Analysis
  • Introduction to Limits
  • One-Sided Limits and Continuity
  • Applications of Limits and Continuity in Business and Economics

 

  1. Differential Calculus
  • Introduction to the concept of Derivative
  • Techniques of Differentiation
  • Relative and Percentage Rate of Change
  • Second and Higher Order Derivatives
  • Application of Derivatives
    • Marginal Analysis
    • Elasticity of Demand
  • Increasing and Decreasing Functions
  • Concavity and Points of Inflection
  • Modelling and Analyzing Optimization Problems in Business and Economics

 

  1. Calculus of Several Variables
  • Functions of Several Variables
  • Introduction to Partial Derivatives
  • Application of Partial Derivatives
    • Marginal Analysis
    • Nature of Commodities
    • Elasticities of Demand
    • Cobb-Douglas Production Function
  • Optimization of Functions of Two Variables in Business and Economics

 

  1. Integral Calculus
  • Introduction to Anti-derivatives
  • Techniques of Integration
    • Substitution Method
    • Integration by Parts Method
    • Partial Fraction Method
  • Applications of Integration to Business and Economics
    • Determination of Cost and Revenue from Marginal Functions
    • Determination of Maximum Profit from Marginal Cost and Marginal Revenue Function
    • Determination of Demand Function from Elasticity of Demand
  • Definite Integrals - Consumer Surplus and Producer Surplus

 

  1. Transportation and Assignment Problems
  • Introduction to Transportation and Assignment Problems
  • Solution of Transportation Problem
    • North-West Corner Method
    • Least Cost Method
    • Vogel’s Approximation Method
    • Modified Distribution Method for Optimal Solution
  • Solution of Assignment Problem using Hungarian Method
  • Solution of Transportation and Assignment Problems using Excel

 

  1. Decision Analysis
  • Introduction to Decision Making
  • Steps in Decision Making
  • Decision Making Environments
    • Decision Making Under Certainty
    • Decision Making Under Uncertainty
      • Maximax Criteria
      • Maximin Criteria
      • Hurwicz Criteria
      • LaPlace Criteria
      • Minimax Regret Criteria
    • Decision Making Under Risk
  • Decision Trees

 

Reading List:

  1. Essential Reading
    • Render, B. Ralph, M. S. JR & Michael, E. H. (2007). Quantitative Analysis for Management. (9th). Prentice Hall of India Pvt Limited.
    • Hoffmann, Bradley, Sobecki, & Price. (2013). Calculus for Business, Economics and the Social and Life Sciences (11th). McGraw-Hill.
    • James, S. (2010). Calculus: Concepts and Contexts. (4th), Richard Stratton.
    • Thukral, J.K. (2013). Mathematics for Business Studies (17th ed.), Scholar Tech Press. Gurgoan.

 

  1. Additional Readings
    • Lial, Greenwell, Miller. (1998). Finite Mathematics and Calculus with Applications. (5th ed.). Addison Wesley Longman, Inc.
    • Taha, H.A. (n.d.). Operations Research: An introduction.
    • Teresa Bradley. (2013). Essential Mathematics for Economics and Business. (4th). John Wiley & Sons Ltd.
    • Sharma, J.K. (n.d.). Quantitative techniques for managerial decisions, Macmillan Publishers India Ltd.

 

Date: July, 2017
Royal Thimphu College