Throughout MOOCOR, one issue is constantly highlighted: we are interested in not only how the procedures are performed but also the concepts that those procedures are built upon them. If we trained ourselves to build our knowledge based on those concepts we would not need to memorize details of algorithms and special cases associated with one. For example, if one conceptually know how to find the solution to a linear system of equations by progressively creating smaller problems based on original problem, say by substitution, then the only remaining thing is to practice and through practice develop efficient ways to solve different problems.

This approach would also help developing a keen sense of knowing when there are mistakes or inconsistencies in the solution approach. Thus instead of trying to finish a work that due to mistakes would lead to incorrect answers, one can evaluate each completed step before going forward.

In Topics 1 and 2 we will restrict ourselves to problems of two dimensions so we can plot them and visually inspect some important concepts related to optimization. As we extend to multi variable problems where no visual inspection is possible, same concepts are useful in our understanding of the features of the problem. For example, the intersection of two line in a two dimensional problem is the solution for a linear system of equations represented by those two lines, while the intersection of three planes in three dimension and intersection of n hyper planes in n dimension in the solution of linear system of equations in 3 and n dimensions respectively.

Learning Goals of Topic 1

  • The ability to plot lines in two dimensional Cartesian coordinate system
  • Understanding and having the ability to identify solutions of linear equations and inequalities
  • The ability to identify solutions to a system of linear inequalities (feasible region)
  • Understanding the features of feasible region and its extreme points in terms feasible and infeasible extreme points and their significance in overall scheme of optimization
  • Understanding the concept of an objective function and its role in a linear programming (LP) model
  • Recognizing the general models of LP

Study Guide

  • Watch Topic 1 video (26:53 minutes). Somewhere around minute 9:00 a reference is made to another video on my channel (Line Plot), pause Topic 1 video and on a new window watch the other video. Upon completion return to the Topic 1 video and resume watching.
  • Visit the Operations Research course on my Web site. On the sliding panel on the left hand side click on "Archive" and select "Solved Problems". In the solve Problems window click on "Graphical Method" to see a number of solved problems. Browse through the problems an get a feel about the type of problems that you may encounter. Try to see whether you can plot the feasible region without the help of any software. Use graph papers and try to be as accurate as you can.
  • On the same Archive tab, select "Topic Archive" and in the new window browse through past semesters of OR class and see whether you can find topics that are related. You should be looking for topics that come under "Plotting feasible region" and visit some of them.
  • Try to do one of the assignments in one of the Topic Archive pages. If you have a problem, post your question to the group.
  • Select one of the problems of your choice and solve it. Between Friday and Saturday post your solution to the group (only PDF files please). If you have not finished your homework, do not look at posted solutions. On Sunday, a test problem will be posted, pick up the problem and try to do it in the allotted time. Participate in the discussion that would follow a couple of days after the test.


  • Did you complete the homework correctly within the required time? If not, what were the major reasons.
  • While solving homework, did you have redo some work or make corrections to some of the values calculated? If so, would you categorize them as careless mistakes or conceptual mistakes? Do you feel that they might be the type of mistakes other participants make? What advice you can give others to reduce the possibility of those mistakes?
  • Did you finish the test within the time identified for the test? If not, how many more minutes it took you to finish the test? Did you finish the test correctly? With passing threshold of 70% did you pass the test? What was the concepts in the test that were not discussed in video tapes, homework, or solved problems? Were they type of concepts that could be deducted from other concepts discussed in Topic 1?
  • About the course: Did you have difficulty finding and studying the materials for this course? How can it be improved?

Additional Resources 

Many resources are available on the Internet in terms of Web document pages, PDF documents and videos. Some of these links are can also be found on my Operations Research Web page. Additionally, there are major mathematics and engineering software that perform many calculations necessary to solve LP problems or solve them completely. Professional software such as MAPLE, MATLAB, MATHEMATICA, ... have such capabilities. Some specific software designed for solving LP problems are also available. Some commercial software such as LINDO also have free student/demo version that can handle problems in limited size that are generally well beyond the sizes required in academic environments. Finally, some of the Internet pages contain scripts and programs that will allow soling LPs on line. You can see an example of this, related to Topic 1 materials in Finite mathematics utility: linear programming grapher page which allows users to enter their LP and plot the feasible region and more. In any case do not forget that my YouTube channel has several videos related to this topic as well.

Professional Organizations 

INFORMS is the professional society for researchers and practitioners of OR. It has hundreds of resources on its Web site that can help introduce the field to interested people. In one of its pages under Related Societies it provides an extensive link to other societies around the world that perform similar services.

More Information  

MOOCOR | Go to | Topic 2