Module                       : BMS 204: Quantitative Techniques

Programme                : BBA

Credit Value              : 12

Prerequisite                : None

General Objectives: 

• develop student’s competence in applying mathematical knowledge and skills in appropriate real world situations;
• Provide students the basic understanding of important quantitative tools and their elementary applications to business problems.
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Learning outcomes: 

Upon successful completion of the module, student is expected to:

• Explain the matrices and determinants
• Formulate and solve linear programming problems
• Apply transportation method of solution
• Solve the problems related to leasing capital expenditure and bond

CONTENT

Unit-I:  Matrices and Determinants                                                                               (10 Hours)

Matrix: meaning.  Types of matrices, Algebra of matrices, Determinants.  Evaluation of determinants (up to order 3).  Properties of determinants, minors and cofactors, adjoint of a square matrix, inverse of a square matrix,  elementary row operations, solution of systems of linear equations (involving not more than three variables) with the help of matrices and determinants. Applications of matrix algebra to business and economic problems; applications of systems of linear equations, Input-Output analysis.

Unit- II: Linear Programming                                                                                        (20 Hours)

Formulation of linear programming problems (LPP), solution to LPPs using graphic method, cases of unique and multiple optimal solutions, unbounded and infeasibility, redundant constraint.

Solution to LPPs using Simplex method – maximization and minimization cases, Shadow prices of the resources. Identification of unique and multiple optimal solutions, unbounded solution, infeasibility and degeneracy.         

The dual problem, Formulation of the Dual. Primal–Dual solutions (excluding solution of dual problem when the primal problem involves mixed constraints).    

Unit- III: Transportation and Assignment Problems                                                   (10 Hours)

The transportation problem: A special linear programming problem.  The transportation method of solution. Methods for finding an initial solution: Northwest corner method, least cost method, Vogel’s Approximation Method (VAM), The Modified Distribution Method (MODI) for finding the optimal solution. The assignment problem, The Hungarian method of assignment.  

Unit- IV: Mathematics of Finance                                                                                  (10 Hours)

Simple and compound interest, rates of interest – nominal, effective and continuous – and their inter-relationships.  Rates of discount and their inter-relationships.  Compounding and discounting of a sum using different rates.  Types of annuities (ordinary, due, deferred, perpetual, etc) and their future and present values.  Amortization of loans.  Problems relating to leasing, capital expenditure and bonds, sinking fund.  

Teaching Strategies

• Lecture
• Demonstration
• Case studies
• Group work

Assessment

·           Assignment                            20 %

·           Mid- Semester Exam              30 %

·           End- Semester Exam              50 %

                                           Total 100 %

Essential Texts

1. Thukral, J.K. Mathematics for Business Studies, New Delhi, Mayur Publication.
2. N.D. Vohra, Quantitative Techniques

References

1. Thukral, J.K. Mathematics, 4^th edition, Taxmann Allied Services Pvt. Ltd.
2. Ayres, F.J. Theory and Problems of Mathematics of Finance, Schaum’s Outline Series.  Tata McGraw-Hill Publishing Co.
3. Wikes, F.M. Mathematics for Business, Finance and Economics, Thomson learning.
4. Budnick, P. Applied Mathematics. McGraw Hill.
5. Mizrahi and Sullivan, Mathematics for Business and Social Sciences. John Wiley and Sons.
6. J.J. Lerner, P. Zima, Theory and Problems of Business Mathematics, Schaum’s Outline series, McGraw Hill.