Module Identifier MBM1810
Module Title QUANTITATIVE METHODS (OPTIMISATION)
Co-ordinator Dr John A Lane
Semester Intended for use in future years
Next year offered N/A
Next semester offered N/A
Course delivery Lecture   20 Hours
Seminars / Tutorials   4 x 1 hour tutorial. Each student is required to attempt regular assignments.
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours  100%

#### Learning outcomes

On successful completion of the module students should be able to:
• formulate linear programming problems and solve simple problems graphically;
• interpret the output from computer software in more complex problems;
• sum geometric series and solve investment and lending problems;
• manipulate polynomial functions and solve equations involving polynomials of low degree;
• find an equilibrium point and determine its stability;
• differentiate simple functions and find the maxima and minima of a function of one and two variables;
• integrate simple functions, use integration to evaluate the area under a curve and interpret the result in economic or business contexts;
• evaluate and interpret marginal, total and average cost or revenue functions.

#### Brief description

The purpose of the course is to demonstrate the usefulness of quantitative methods in situations that arise in industry and business. The underlying mathematics is introduced and related to topics including optimisation of functions representing profit, costs, etc; calculations for investment problems; equilibrium states for supply and demand; and relationships between functions such as average, total and marginal cost/revenue .   The emphasis throughout is on the application of mathematical techniques to situations that arise in business and industry and the ability to make appropriate deductions from the results.

#### Content

1. Linear Programming: Formulation. Graphical solution for two variables. Sensitivity analysis. Interpretation of computer output for multi-variable problems.
2. Investment Problems: Compound interest; effective interest rate, present value. Geometric series; regular investments, annuities.
3. Supply and Demand Functions: Equilibrium price; solution of equations, stability. Differentiation of polynomial functions; maximum and minimum. Relation between marginal, total and average; integration. Elasticity. Two variable problems, Lagrange multipliers.