Welcome to the Course Page of
MATH 3171 3.00 A

Linear Optimization

Summer 2015

Department of Mathematics and Statistics
Faculty of Science
York University
4700 Keele Street
Toronto, Ontario  M3J 1P3

Course Organization:


Course Information

Course Schedule


Exams Information

Links & Other Resources


This area will contain announcements and solutions to the tests and assignments. Announcements made in class will be posted here in reverse chronological order and will not be repeated in class. Please take a minute to read the announcements carefully, as they often get updated. You may need to Reload/Refresh this page.

July 12:

Please  click here  to see your final exam mark and unofficial letter


grade for the course. Please also note that your official grade for the


course will be available by the Registrar's Office upon the faculty





June 27:

As it was announced in the class on Wednesday, the Final Examination


for the course will take place on Tuesday, June 30 from 19:00 to 22:00 in


ACW 205. The exam will be comprehensive, covering the entire course


material according to the  Course Schedule  but with an emphasis on the


more recent material. If less common formulas are needed on the exam,


then those will be provided on the exam. There will be several questions,


some with a few parts. Marks for each question will be indicated. You will


have to show all your work, and explain your solutions where appropriate.


Please also note that I will be holding an additional office hour for last


minute questions on Tuesday, June 30 from 13:00 to 14:00.

June 26:

According to your request, I am making available  solutions  to selected


Homework Problems from Section 4.13 of the textbook in the PDF format.

Please note that the graded Test #2 papers will be returned in the class on


Monday, June 29. I am making available the scanned copy of  solutions


to the test questions in PDF format.

June 24:

Homework problems for Chapter 6:


Section 6.1 # 1, 2, 3, 5 (each Radio 2 requires 1 (not 2) Laborer-2 hour);


Section 6.2 # 1, 2;


Section 6.3 # 1, 2, 3, 4, 5.

June 22:

As it was announced in the class today, we will write Test #2 during


the first half of the lecture period on Wednesday, June 24.


On the test you will be responsible for all the material covered in class


from Sections 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11 and


4.12 of the textbook.

June 21:

According to your requests, I am making available  solution  to the


Homework Problem from Section 4.10 of the textbook in the PDF format.

June 18:

Please note that the student course evaluations are available on-line


at the URL link:  http://courseevaluations.yorku.ca  until Monday,


June 29, 2015. It is the time for you to be the judge. Please go on-line


and complete the course evaluation.

June 14:

According to your requests, I am making available solutions to the


Homework Problems from Section 4.4 of the textbook in the PDF format.


Please note that the graded Test #1 papers will hopefully be returned in the


class tomorrow.

June 12:

I am making available the weekly  schedule  of the Math Lab for Summer.

June 08:

As it was announced in the class today, we will write Test #1 during


the first half of the lecture period on Wednesday, June 10.


On the test you will be responsible for all the material covered in class


from Sections 3.1-3.6, 3.8-3.11, 4.1 and 4.2 of the textbook.

June 07:

According to your requests, I am making available solutions to selected


problems from Sections 3.2, 3.8, 3.10 and 3.11 of the textbook in the PDF



June 05:

According to your requests, I am making available solutions to selected


problems from Sections 3.8 and 3.9 of the textbook in the PDF format.

June 03:

Homework problems for Chapter 4:


Section 4.1 # 1, 2, 3; Section 4.4 # 1, 2, 4, 6, 7;


Section 4.5 # 1, 2, 3, 4, 5; Section 4.6 # 1, 4; Section 4.7 # 1, 2, 9;


Section 4.8 # 1, 4, 5, 6; Section 4.10 # 4; Section 4.11 # 1, 2, 4;


Section 4.12 # 1, 2, 4, 5; Section 4.13 # 1 (1, 2, 4, 5), #2;


Section 4.14 # 1, 2, 4; Section 4.16 # 6, 7;


Chapter 4 Review Problem # 19.

May 27:

Please download the Trial Version of LINDO to your PC using the link:


Download free trial version of LINDO package


Please note that you may also use the package in the Gauss Lab at S110 Ross.

May 20:

Welcome back!


To view and/or print PDF files you need to download the Acrobat Reader  


Homework problems for Chapter 3:


Section 3.1: #2, 3, 5; Section 3.2: #4, 5, 6; Section 3.3: #2, 3, 6, 9;


Section 3.4: #1, 3; Section 3.5: #1, 6; Section 3.6: #4;


Section 3.7: #1; Section 3.8: #1, 4,10; Section 3.9: #1, 12;


Section 3.10: #1, 9; Section 3.11: #4, 9.

Course Information:



S1 2015





Lectures (day, time and venue):

M/W 18:00 – 21:00, TEL 1004



Dr. Iouldouz Raguimov



S512 Ross






416-736-2100, Ext. 66092


Office Hours:

T 13:00-14:00, W 16:00 – 17:00, also by appointment








Two Class Tests:

25+20% of the overall grade for the course


Final Examination:


Course Description: Linear Optimization is an introductory course in Operations Research. The course introduces students to linear optimization (linear programming), including the problem formulation, simplex method, LP-duality theory, sensitivity analysis, and its business and industrial applications. With the help of notes and class instructions students will be introduced to the optimization solver software LINDO/LINGO and the spreadsheet. For a more detailed list of topics with references to the textbook, please see Course Schedule.


Operations Research: Applications and Algorithms, Fourth Edition

by Wayne L. Winston 


Books/Cole, Thomson, 2004. ISBN 0-534-42358-2

Optional Aids:

Student Solutions Manual for Operations Research, Fourth Edition


by Wayne L. Winston


Books/Cole, Thomson, 2004. ISBN 0-534-42360-4


Course Prerequisites:

SC/MATH 1021 3.00 or AP/SC/MATH 1025 3.00 or SC/MATH 2221 3.00,


plus SC/CSE/COSC 1520 3.00 or SC/CSE/COSC 1540 3.00 or


SC/CSE/COSC 1020 3.00 or equivalent. Students who do not have the


prerequisites must see me within the first two weeks of the classes.



Course Credit

SC/MATH 2751 3.00, AP/ECON 3120 3.00, AP/ADMS 3331 3.00,


AP/ADMS 3351 3.00, GL/MATH 3660 6.00, CS/MATH 3170 6.00.


Important Dates:

May 19: Classes commence

May 25: The last date to enrol in the course without my permission

June 02: The last date to enrol in the course with my permission

June 16: The last date to drop the course without receiving a final grade


June 29: Classes end

June 30-July 03: Final examination, TBA.

Course Schedule:
(subject to any changes announced in class)




May 19-22

Introduction, Ch.1, 3.1, 3.2

Classes begin on Wednesday, May 20. 

May 25-29

3.3, 3.4, 3.5, 3.6, 3.8


June 01-05

3.9, 3.10, 3.11, 4.1, 4.2

June 08-12

4.3, 4.4, Test #1, 4.5

Test #1 will take place on Wednesday, June 10.

June 15-19 

4.6, 4.7, 4.8, 4.9, 4.10


June 22-26 

4.11, 4.12, 4.13, Test #2, 4.14

Test #2 will take place on Wednesday, June 24. 

June 29 

6.1, 6.2, 6.3, Review


June 30

Final Examination

Room TBA.

Note: The course will not cover all the sections of the chapters of the textbook.


Throughout the term, homework problems will be posted to the Announcements Section of the course web page. In order to develop your understanding of the course material you must do all assigned problems. These will not be collected for grading and hence will not directly affect your grade. However, it is extremely important that you complete all assigned exercises. Do not memorize them. Rather, learn how to solve problems like them. Learning Mathematics is not a spectacular sport, it is a participatory event. There is nothing like a bit of computation to strengthen understanding in mathematics! Use the Solutions Manual only after you have tried the problem. Successful students must keep up with homework and seek help for points they do not understand as soon as possible. Do not fall behind! It is recommended to read the relevant sections of the textbook before every class. Next to the classes, working out the answers to the problems is the most important preparation for the tests and exam that will contain for the most part but not exclusively, questions very similar to those from the textbook. It is quite practical to work on your own or together in small groups. Each student should do at least three hours of independent study for every lecture hour. The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend working on problems.
Note: Help is also available in the Math Lab in S525 Ross.

Exams Information:

Lecture/Exam Rules:

All internet connected and other distractive electronic devices (cell phones, pagers, head phones, digital dictionaries, CD players, laptops) need to be turned off during class, i.e. during lectures, tutorials, tests and exams. All such devices as well as all books, papers, knapsacks, and briefcases must be left at the front of a lecture hall during tests and exams. Anyone caught with electronic devices will be charged with Academic Dishonesty (see the next page). The only items you may have at your seat during exams and tests are pens, pencils, eraser, nonprogrammable, nongraphing calculators, student ID and purses. Notes need to be taken manually; use of cellphone cameras in class is not allowed. You are responsible for all material covered in lectures.
Note: Photo identification and signing-in are required at all tests and exams.

Final Grade:

The official grades at York University are LETTER grades. Qualitative descriptions of these grades can be found in the York Calendar at this link. Your test marks will be on a numerical scale because these have to be weighted and averaged in various ways, but THERE IS NO AUTOMATICPREDETERMINED CORRELATION BETWEEN NUMERICAL GRADES AND LETTER GRADES in this course. In particular, the "numerical" grades you receive are NOT to be interpreted as percentages; they are merely 'raw scores'. When the tests are returned in class, the distribution of'raw scores' will be announced along with an approximate conversion to letter grades. The median letter grade for the course will likely fall between C and C+. 
The composition of the final grade is as follows:
Two Tests (80 minutes each written tests held in lecture periods): 25+20% (Tentative dates for the tests: Wednesdays, June 10 and June 24, 2015);
Final Examination 
(three-hour exam scheduled by the Registar's Office): 55% of the overall grade, will take place during the examination period.
 Students have five days from the date of the return of test papers to appeal their marks. Some test papers (randomly selected) are photocopied before they are handed back, so we can detect subsequent alterations.

Make-up Policy:

No permission will be given to a student to write tests in advance of their scheduled dates. No make-up will be done for the tests. A missed test will be counted as zero, except under extreme circumstances in which case the corresponding percentage of the overall grade will be "forwarded" to the final exam. If you miss a test for medical reasons, you must turn in within one week following the test date the Attending Physician's Statement form provided here after getting it filled in by your doctor. No other type of medical note will be accepted. However, missing tests is extremely dangerous and not recommended. As experience has shown, students who miss class tests because of some 'mysterious illnesses' will usually average 30% on the final exam.
Student who misses the final examination will be allowed to write a make-up exam only if both of the following conditions are met:
the student notifies me (raguimov@mathstat.yorku.ca) or the Department of Mathematics and Statistics (Undergraduate Office, N502/503 Ross Building, 416-736-2100, Ext. 55902 or 33969) in advance that the exam will be missed;
 the student submits within one week following the exam date the Attending Physician's Statement form provided here after getting it filled in by his/her doctor.
Students who miss the final examination and do not meet both conditions will receive a grade of F. It is student's responsibility to fill out and submit the Deferred Standing Agreement form.
Note: Do not make vacation/job plan until the final exam date is known: having a plane ticket for Banff or Hawaii on June 30 is NOT a legitimate excuse for absence from a final exam on July 02.

Religious Observance:

Special needs students, please identify yourselves to the course instructor as soon as possible. York University is committed to respecting the religious beliefs and practices of all members of the community and making accommodations for observances of special significance to adherents. If any of the dates specified in the course schedule for in-class tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) within the first week of classes. Please note that if the final exam date poses a conflict, students must complete the Final Exam Accommodation form, which can be obtained from the Registrar’s Office. Please note that York University welcomes feedback on accessibility issues. Your feedback may be provided by sending e-mail to: mathstat@yorku.ca

Academic Honesty:

Students are responsible for familiarizing themselves with University Policies and Regulations. Conduct that violates the ethical or legal standards of the university community or of one’s programme or specialization may result in serious consequences. Refer to the Senate Policy on Academic Honesty. Photo identification and signing-in are required at all tests and exams. Also, some test papers (randomly selected) will be photocopied before they are returned so that subsequent alterations can be detected.


Individual questions can be discussed by e-mail or in person after class, or during office hours. Please send all e-mail notes as plain text within the body of the message. Do not send attachments or HTML-formatted e-mail. No texting, please. Also, if the name of your account is an alias, I will not know who the mail is from unless you sign it; it also risks being accidentally discarded as junk mail. The course web page will be up-dated regularly to include important announcements made in class, such as the material to be covered on the tests. E-mail notes requesting such information contained on the web page will be answered the last.

Links and Other Resources:

1- York Undergraduate Mathematics Program
2- York University Library
Infinity Club
- Online Forum
- Download free trial version of LINDO package
- Download free trial version of LINGO package
7- Local time in Toronto

Questions and comments regarding this Web page please send to raguimov@mathstat.yorku.ca

© 2006-2015, All Rights Reserved, York University & Iouldouz S. Raguimov

Last updated on July 12, 2015