### Reminder

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 them. 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, 2, and 3 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 3

• The ability to extend the knowledge gained in Topics 1 and 2 as a basis to explore ideas for new topic
• Gaining the ability the ability to write the full LP, given a feasible region in two dimensional space
• Understanding the concepts basic and non-basic variables and their relationship to the extreme points of the feasible region
• Integrating the knowledge gained in Module 1 to develop an overall scheme for solving LPs
• Gaining insight into some special cases of LPs

### Study Guide

• Watch Topic 3 videos, Part 1 (25:21 minutes) and part 2 (13:55 minutes).
• Watch additional videos on my YouTube channel if you need additional lectures. Some of the ones related to Module 1 materials are: Basic and Non-basic Variables, Feasible Region and Extreme Points (28:49 min), Sample Solved LP Problem - Graphical and Simplex Method (7:13 min), and four videos on working with available software LINDO and LiPS.
• 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 write the LP of a given feasible region and whether you can identify associated basic and non-basic variables of the extreme points of a given LP and its associated feasible region. Also verify that on adjacent extreme points only one variable from basic solution is replaced by one variable from non-basic variable set at that extreme point.
• 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", "Graphical solution", "Developing constraint set from a given plotted feasible region", or related topics 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 Wednesday and next Sunday post your solution to the group (only PDF files please). If you have not finished your homework, do not look at posted solutions. On Monday, 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.

### Assessment

• Did you complete the homework correctly within the required time? If not, what were the major reasons.
• While solving homework, did you have to 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 Topics 1, 2 and 3?
• About the course: Did you have difficulty finding and studying the materials for this course? How can it be improved?