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Next: MC223 Relativity Up: Year 2 Previous: MC215 Software Engineering Project

MC222 Optimisation


MC222 Optimisation

Credits: 10 Convenor: Dr. M.J. Phillips Semester: 1 (weeks 1 to 6)


Prerequisites: essential: MC126, MC147
Assessment: Continuous assessment: 20% One and a half hour examination: 80%

Lectures: 18 Classes: 5
Tutorials: none Private Study: 52
Labs: none Seminars: none
Project: none Other: none
Total: 75


Explanation of Pre-requisites

MC126 presents the methods for calculating properties of curves such as gradient at a point.

MC147 presents techniques for solving systems of linear equations.

Course Description

A typical problem arising when mathematics is applied to practical situations is to minimise the cost of achieving some task subject to various constraints. By the end of the course the student should be able to correctly formulate problems mathematically, from verbal descriptions, and be able to solve simple cases.

Aims

To enable the student to understand the formulation of problems involving linear constraints and how to optimise such problems using a linear objective function by linear programming.

To present both the theoretical reasons for the methods and the numerical methods for solving problems with linear programming.

Objectives

To formulate an optimisation problem in the form of a linear programming problem.

To understand the properties of extrema.

To be able to calculate feasible and basic feasible solutions.

To understand the use of the Simplex Method and Two Phase Simplex Method.

To be able to use the Duality Theorem to solve linear programming problems.

To be able to use Lagrange multipliers to solve a constrained optimisation problem.

Transferable Skills

The ability to formulate an optimisation problem in the form of a linear programming problem.

The ability to calculate feasible and basic feasible solutions and hence be able to use the Simplex Method, Two Phase Simplex Method and the Duality Theorem to solve linear programming problems.

Knowledge of Lagrange multipliers to be able to solve a constrained optimisation problem.

Syllabus

Formulation of linear programs. Systems of linear inequalities. Properties of extrema. Feasible and basic feasible solutions. Simplex Method. Two Phase Simplex Method. The Duality Theorem. Dual Simplex Method. Game Theory. Use of Lagrange multipliers.

Details of Assessment

The final assessment of this module will consist of 20% coursework and 80% from a one and a half hour examination during the January exam period. The 20% coursework contribution will be determined by students' solutions to coursework problems. The examination paper will contain 4 questions with full marks on the paper obtainable from 3 complete answers.


next up previous
Next: MC223 Relativity Up: Year 2 Previous: MC215 Software Engineering Project
S. J. Ambler
11/20/1999