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Up: Year 2
Previous: MC215 Software Engineering Project
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 Prerequisites
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: MC223 Relativity
Up: Year 2
Previous: MC215 Software Engineering Project
S. J. Ambler
11/20/1999