Module Overview

Linear Programming

This module expands on the fundamental concepts of linear programming covered in MATH 2804. It introduces
artificial variables as a means to finding an initial basic feasible solution, and the concept of duality. The
fundamental theorem of linear programming and the theory behind the simplex method are presented. Case
studies will be presented, formulated and solved using appropriate software.

Module Code

MATH 4809

ECTS Credits


*Curricular information is subject to change

Linear Programming Concepts
Feasible, basic feasible and optimal solutions. The fundamental theorem
of linear programming.
Simplex method (tableau)
Standard form, canonical form. Basic and nonbasic variables, pivot rows and columns, ratio test. Artificial
variables, tests for optimality.
Revised Simplex
Matrix and vector form, reduced costs, ratio tests.
Marginal costs/prices, formulations, weak duality theorem, strong duality theorem.
Sensitivity Analysis
Finding parameter ranges using revised Simplex and relationships of the primal and the dual, solving problems
relating to economic analysis.
Complementary Slackness
Quantifying the relationship between the primal/dual slack variables and dual/primal slack variables, proving
optimality of primal/dual.

Lectures supported by tutorials

Module Content & Assessment
Assessment Breakdown %
Formal Examination100