MAU34802 The theory of linear programming
| Module Code | MAU34802 |
|---|---|
| Module Title | The theory of linear programming |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Pierre-Yves Bienvenu |
| Module Prerequisites | MAU11100 Linear algebra |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- If necessary, a failed exam is reassessed by an exam in the reassessment session, and failed continuous assessment is reassessed by one or more summer assignments in advance of the supplemental session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
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.