# LINEAR PROGRAMMING AND PROBABILITY

STM3LPP

2017

Credit points: 15

## Subject outline

Linear Programming and Probability is a subject with many important real word applications. It is suitable for students taking majors in mathematics, statistics, physics or engineering. Linear Programming involves maximising and minimising a linear function subject to a finite number of linear constraints. This subject also gives an introduction to Game Theory, which deals with decision making in a competitive environment; game theory uses ideas from probability theory combined with the tools of linear programming. The subject also details how linear programming can also used to perform special probability computations, such a regression, and selection of probability distributions.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorTomasz Kowalski

Available to Study Abroad StudentsYes

Subject year levelYear Level 3 - UG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites MAT2LAL OR STM2PM

Co-requisitesN/A

Incompatible subjects MAT3LPG

Equivalent subjectsN/A

Special conditionsN/A

## Graduate capabilities & intended learning outcomes

01. Solve linear programming problems graphically.

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

02. Employ the simplex method.

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

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

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

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

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

05. Undertake sensitivity analysis on linear programming problems.

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

06. Solve 2 player zero sum games.

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

07. Use linear programming to do regressions using the norm.

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

08. Use linear programming to choose between two probability distributions.

Activities:
Online reading materials and videos. Collaborative problem solving classes using Practice Sheets.
Related graduate capabilities and elements:
Literacies and Communication Skills (Writing,Quantitative Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

## Subject options

Select to view your study options…

Start date between: and    Key dates

## Bendigo, 2017, Semester 2, Blended

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorTomasz Kowalski

### Class requirements

Directed Reading Week: 31 - 43
One 8.0 hours directed reading per week on any day including weekend during the day from week 31 to week 43 and delivered via online.
"The subject will be blended, with a fully comprehensive LMS site, with required weekly materials, "key concept videos", recordings of worked examples, and supplementary support materials available. This material, together with participation in the on-line forum, should constitute 8 hrs per week."

Practical Week: 31 - 43
Two 1.0 hours practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
"The online materials will be integrated with 2 weekly 1 hour face-face classes, focused around weekly Practice Sheets."

### Assessments

Five 300-word Written Assignments40 01, 02, 03, 04, 05, 06, 07, 08
One 2hr written Examination60 01, 02, 03, 04, 05, 06, 07, 08

## Melbourne, 2017, Semester 2, Blended

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorTomasz Kowalski

### Class requirements

Directed Reading Week: 31 - 43
One 8.0 hours directed reading per week on any day including weekend during the day from week 31 to week 43 and delivered via online.
"The subject will be blended, with a fully comprehensive LMS site, with required weekly materials, "key concept videos", recordings of worked examples, and supplementary support materials available. This material, together with participation in the on-line forum, should constitute 8 hrs per week."

Practical Week: 31 - 43
Two 1.0 hours practical per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
"The online materials will be integrated with 2 weekly 1 hour face-face classes, focused around weekly Practice Sheets."