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 feasable 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.

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.

Methods for solving linear programming problems based on the Simplex
Algorithm of George Danzig.

The Transportation Problem

The Karush-Kuhn-Tucker Conditions characterizing optimal
solutions of nonlinear programming problems.

Mathematical models of simple exchange economies.

Leontieff models.

Module Prerequisite

MA1212 (Linear Algebra II).

Assessment Detail

This module will be examined in a 2-hour examination
in Trinity term.