Module Identifier MA33110  
Academic Year 2004/2005  
Co-ordinator Mr Alan Jones  
Semester Semester 2  
Pre-Requisite MA21410  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

On completion of this module, a student should be able to:

General description

The basic problem of Linear Programming is to maximise or minimise a linear function of several variables, subject to constraints expressed as linear inequalities or equations. The theory of Linear Programming is now well established to the extent that the technique often appears as an option in widely available business computer packages such as spreadsheets. This module provides a balance between the theory and applications of the subject and considers the interpretation of problem solutions.


To introduce an important and widely used application of Mathematics in the real world.


1. INTRODUCTION TO LINEAR PROGRAMMING: Problem formulation and the breadth of application. Basic definitions, including convexity, extreme points, feasible solutions, basic solutions, basic and non-basic variables, basic feasible solutions.
2. THE SIMPLEX METHOD: Overall idea; geometrical and algebraic characterisation. Fundamental Theorem of Linear Programming. Artificial variables; big-M method, two-phase method, Dual Simplex method. Unsigned variables. What can go wrong.
3. SENSITIVITY ANALYSIS: Interpreting the simplex tableau, including economic interpretations where relevant. Dual prices. Marginal change and return.
4. DUALITY: The dual problem and its motivation. Fundamental Theorem of Duality. Relationships between solutions to the primal and dual problems. Complementary slackness. Interpretations of the Dual problem.
5. SPECIAL TOPICS: A selection of topics from: Zero-sum games, Integer programming, Assignment problems, Transportation problems.

Reading Lists

** Supplementary Text
J G Ecker & M Kupferschmid (1988) Introduction to operations research Wiley 0471884456
H A Taha (2003) Operations research: an introduction 7th. Prentice Hall 01300488089
W L Winston (1995) Introduction to mathematical programming: applications and algorithms 2nd. OWS-Kent 0534230466


This module is at CQFW Level 6