STM3LPP Linear Programming and Probability Semester 2, 2022
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Linear Programming and Probability
STM3LPP
Semester 2, 2022
ABOUT THIS SUBJECT
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 be used to perform special probability computations, such as regression, and selection of probability distributions.
SUBJECT INTENDED LEARNING OUTCOMES (SILOs)
Upon successful completion of this subject, you should be able to:
1. Solve linear programming problems graphically.
2. Employ the simplex method moving freely between a proble and its dual
3. Undertake sensitivity analysis on linear programming problems
4. Calculate regressions using the norm, geometrically and via linear programming
5. Solve simultaneous two-player zero sum games using linear programming
LEARNING ACTIVITY SCHEDULE
Week |
Learning Activity |
Contact hours |
1-12 |
Practice classes |
2 |
|
Total |
24 |
*Timetable details are available at http://www.latrobe.edu.au/students/timetables. Students should also regularly check this subject’s LMS site for updated information.
Details of any self-allocation activities: |
|
It is expected that students in classes scheduled for public holidays will complete the work in their own time using resources provided, and seek help from their instance coordinator if needed.
SELF-DIRECTED STUDY
In addition to the learning activities specified, you are expected to allocate approximately 10.5 hours per week of self-directed study in this subject. This time includes subject preparation, completing learning activities, readings, assessment preparation and other related work to enhance your participation in this subject and your learning at La Trobe. This time should not all be spent on completing the assignments. It is suggested that you watch the online videos, finish practice classes, annotate lecture notes (using the recordings if necessary) and review the feedback on previous assignments.
LEARNING RESOURCES & TECHNOLOGIES
Resource Type |
Title |
Year |
Publisher |
Required and provided in electronic form on the LMS |
|||
Subject notes |
Linear programming and Probability |
2018 |
LTU, available on LMS. |
ASSESSMENT AND FEEDBACK SUMMARY
|
Date due |
% |
Assessment Activity (further description) |
Feedback method |
ILOs & Essentials assessed |
1. |
Official semester two exam period |
70 |
Exam |
|
1, 2, 3, 4, 5. |
2. |
Monday of weeks 3, 5, 7, 10 and 11 |
30 |
Five assignments* |
Model answers, marking and comments (through LMS). |
1, 2, 3, 4, 5. |
*Students should keep a copy of all assignments submitted for assessment.
Turnitin is a web-based text-matching software system used at La Trobe University to assist you in writing your assignments and checking for similarity with existing published work. Please remember to allow adequate time for you to submit your assignment to Turnitin. It is your responsibility to have your assignment submitted by the assessment due date. Not receiving an originality report is not an acceptable reason for requesting an assignment extension unless it is a required part of the assessment.
HURDLE REQUIREMENTS
There are a variety of assessment hurdles or conditions for passing a subject other than the overall mark.
Hurdle Requirements may be built into the assessment of the learning outcomes of your subject. There are no Hurdle Requirements for this subject.
SPECIAL CONSIDERATION
If you are not able to complete an assessment task on the scheduled date due to exceptional circumstances beyond your control, you may be eligible for Special Consideration.
If the assessment task is worth 15% or more of the total assessment for this subject and you have experienced serious short term, adverse and unforeseen circumstances that substantially affect your ability to complete an assessment task to the best of your potential, you can apply for Special Consideration. To do this or find more information go to http://www.latrobe.edu.au/special-consideration Please note that the La Trobe University policy regarding special consideration relates only to individual assessment tasks that are worth 15% or more, so in this subject, only the exam. For Special Consideration for assessment tasks worth less than 15% of your total mark, contact the Instance Coordinator.
For Information about Special Consideration policy, go to Special Consideration Policy at
https://policies.latrobe.edu.au/document/view.php?id=205
REQUEST AN EXTENSION OF TIME TO SUBMIT AN ASSIGNMENT TASK
Please note that the La Trobe University policy regarding late submission of assessment tasks relates only to individual assessment tasks that are worth 15% or more. The 5 assignments for this subject are
each worth 6%, therefore decisions regarding late submission of any of these assignments are not governed by this policy.
Late solutions to assignments will not normally be accepted. Exceptions will only be considered where prior arrangement is made with the instance coordinator. Poor time management is not an acceptable reason for an extension.
ACADEMIC INTEGRITY
“Academic integrity means being honest in academic work and taking responsibility for learning the conventions of scholarship. Academic integrity education is integral to the learning experience at La Trobe University. The University requires its academic staff and students to observe the highest ethical standards in all aspects of academic work, and it demonstrates its commitment to these values by awarding due credit for honestly conducted scholarly work, and by penalising academic misconduct and all forms of cheating”. (La Trobe University Academic Integrity – Procedures and Responsibilities, 2015).
While the Department of Mathematics and Statistics encourages discussion amongst students in learning statistics and mathematics, we make a clear distinction between this, and collusion or copying. Producing assignments which should be your own independent work in collusion with and/or using the work of other people is academic misconduct and will be reported through the Subject Co-ordinator to the School Academic Integrity Advisor.
The penalty for contract cheating (submitting an assignment that you paid someone else to do) may be as severe as “exclusion from the University without readmission” . Refer to the Academic Integrity - Schedule of Responses and Penalties for Academic Misconduct at
https://www.latrobe.edu.au/__data/assets/pdf_file/0006/847923/academic-integrity-schedule-of- responses.pdf
You should familiarise yourself with the Academic Integrity website at https://www.latrobe.edu.au/students/admin/academic-integrity, and complete the Academic Integrity Module (AIM) in your LMS.
If you have any questions, ask your Subject or Course Coordinator.
STUDENT FEEDBACK ON SUBJECT SURVEY
The Student Feedback on Subjects (SFS) Survey is one of the quality assurance processes that occur across the University. In this survey, you can tell us about your learning experiences in this subject. We value your feedback. Your views are taken seriously and assist us to improve the learning experience for future students. The surveys are anonymous and will be available prior to the end of the teaching period.
Feedback from previous students who completed this subject is available in the LMS site for this subject. For more information you may contact [email protected].
CHARTER OF STUDENT RIGHTS AND RESPONSIBILITIES
As a La Trobe coursework student, you have a number of rights and responsibilities. La Trobe statutes and regulations, as well as policies and procedures govern your rights and responsibilities. LaTrobe University aspires to provide an outstanding student experience conducive to scholarly activity and supportive of your learning goals.
The Charter of Student Rights and Responsibilities is a brief summary of your rights and responsibilities as a student at La Trobe. The Charter was developed in consultation with La Trobe students. A copy of the Student Rights and Responsibilities can be found at https://policies.latrobe.edu.au/document/view.php?id=225.
STUDENT COMPLAINTS
The Student Complaints Management System (SCM) is a formal mechanism for students to lodge concerns about any aspect of their University experience. A student complaint may be about any aspect of University life, such as an administrative matter, a problem with a subject or course, or the conduct of a student or staff member.
For more information about the Student Complaint process and how to lodge a complaint, visit the Complaints and Feedback page at: https://www.latrobe.edu.au/students/support/complaints.
SCHEDULE
Week |
Lecture |
Notes Ref. |
1. |
Formulating LP problems and using the graphical solution |
Chapter 1 |
2. |
Convex combinations, convex sets, and convex hulls |
Chapter 2 |
3. |
The simplex algorithm. |
Chapter 3 |
4. |
Introducing artificial variables, and implementing the 2 phase and big M methods. |
Chapter 4 |
5. |
Duality, and the duality theorem |
Chapter 5 |
6. |
Sensitivity analysis |
Chapter 6 |
7. |
Expected value |
Chapter 7 |
8. |
Information theory: Discrete entropy |
Separate notes |
9. |
The notion of median, and its use in the facility location problem using the taxicab metric. Graphical and linear programming solutions to the LAD linear regression problem |
Chapters 8 and 9 |
10. |
Introducing game theory, and using linear programming to solve zero sum games. |
Chapter 10 |
11. |
Nash equilibria |
Chapter 11 |
12. |
Revision |
Chapter 12 |
GETTING HELP AND SUPPORT AT UNI
A range of services at La Trobe can assist you with your studies, health and wellbeing.
For the full range of services and facilities available for you, go to Student Help and Support at
http://www.latrobe.edu.au/students/support.
2022-07-12