LINEAR PROGRAMMING AND GAME THEORY

MAT3LPG

2015

Credit points: 15

Subject outline

Linear Programming and Game Theory are relatively new branches of mathematics. Linear Programming involves maximising and minimising a linear function subject to inequality and equality constraints. Such problems have many economic and industrial applications. Game Theory deals with decision making in a competitive environment. This unit studies the simplex technique for solving linear programming problems and gives an introduction to game theory and its applications.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorGrant Cairns

Available to Study Abroad StudentsYes

Subject year levelYear Level 3 - UG

Exchange StudentsYes

Subject particulars

Subject rules

Prerequisites MAT2LAL or MAT2AAL

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Special conditionsN/A

Readings

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsUnit text for MAT3LPGPrescribedPrinted unit text available from University BookshopDepartment

Graduate capabilities & intended learning outcomes

01. Solve linear programming problems graphically.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)

02. Employ the simplex method.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)

03. Use artificial variables, employing the 2 phase and big M methods.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)
Writing (Writing)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Discipline-specific GCs (Discipline-specific GCs)

04. Implement the notion of duality in linear programming and move freely between a problem and its dual.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Writing (Writing)
Discipline-specific GCs (Discipline-specific GCs)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Creative Problem-solving (Creative Problem-solving)
Critical Thinking (Critical Thinking)

05. Undertake sensitivity analysis on linear programming problems.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Critical Thinking (Critical Thinking)
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)
Inquiry/ Research (Inquiry/ Research)

06. Compute the nim value of combinatorial games and determine which player has the winning strategy.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Creative Problem-solving (Creative Problem-solving)
Critical Thinking (Critical Thinking)
Discipline-specific GCs (Discipline-specific GCs)
Writing (Writing)

07. State and use the Minimax Theorem.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Writing (Writing)
Discipline-specific GCs (Discipline-specific GCs)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Creative Problem-solving (Creative Problem-solving)

08. Solve 2 player zero sum games.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Related graduate capabilities and elements:
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)
Writing (Writing)
Critical Thinking (Critical Thinking)

Subject options

Select to view your study options…

Start date between: and    Key dates

Melbourne, 2015, Semester 2, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorGrant Cairns

Class requirements

Lecture Week: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Practical Week: 31 - 43
One 1.0 hours practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Assessments

Assessment elementComments% ILO*
One 3-hour written examination70 01, 02, 03, 04, 05, 06, 07, 08
Six fortnightly written assignments30 01, 02, 03, 04, 05, 06, 07, 08