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MAU34802 The theory of linear programming

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2020-21
Contact Hours
11 weeks, 3 lectures per week
Lecturer
Prof. David Wilkins
Learning Outcomes
On successful completion of this module, students will be able to:
  • determine optimal solutions of simple linear programming problems using the simplex method;
  • justify with reasoned logical argument the basic relationships between feasible and optimal solutions of a primal linear programming problem and those of the corresponding dual programme;
  • explain why the simplex method provides effective algorithms for solving linear programming problems;
  • explain applications of linear algebra and linear programming in contexts relevant to mathematical economics;
Module Content
  • Introduction to linear programming problems.
  • The Transportation Problem
  • Methods for solving linear programming problems based on the Simplex Algorithm of George Danzig.
  • Duality in the theory of linear programming problems.
  • Farkas's Lemma.
  • Applications of Farkas's Lemma to prove duality theorems in the theory of linear programming problems.
  • The Karush-Kuhn-Tucker Conditions characterizing optimal solutions of nonlinear programming problems.
 
Module Prerequisite
MAU11102 (Linear Algebra II).
Assessment Detail
This module will be examined in a 2-hour examination. Continuous assessment will count for 20% and the annual exam will count for 80%. Re-assessments if required will consist of 100% exam.