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.
- Students are assessed based on the exam alone.
- Re-assessment, if needed, consists of 100% exam.
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.