## MATH 21-292: Operations Research

### Announcements

Here is the course syllabus.

*******Midterm 1 will be held on Friday February 23 in class*******

Here is a list of topics that you should know for the first midterm. Here is the first midterm from 2016 with solutions

These are videos giving examples of how to show a set is convex and how to set up the Big M method.
### Schedule

Week 1: Hillier and Lieberman 3.1-3.4

Week 2: The simplex method. Hillier and Lieberman 4.1-4.4 along with some theory.

Week 3: Mathematical theory of the simplex method, pitfalls of the simplex method, big M method. Hillier and Lieberman 4.5-4.6

Week 4: Two-phase method, postoptimality analysis. Hillier and Lieberman 4.6-4.7

Week 5: The simplex method via matrices. Hillier and Lieberman chapter 5

Week 6: The fundamental insight and midterm 1
### Homework

All homework exercises are from Hillier and Lieberman 10th edition unless otherwise noted. If you have a different edition of the book, the exercises may be different! Please check with me
or a colleague to make sure you have the correct problems.

**Homework 1** (due Friday January 26 in lecture): 3.1-5, 3.1-9, 3.1-13, 3.4-14(a), given a linear optimization problem with 2 decision variables and a non-empty and bounded feasible
region use
the
graphical method to sketch a proof that an optimal solution lies on a corner point.

**Homework 2** (due Friday February 2 in lecture): 4.1-6, 4.3-4, 4.3-7, 4.5-8

**Homework 3** (due Friday February 9 in lecture): 4.6-2 (a) and (c)-(e), 4.6.5 (a) and (c), 4.6-9 (a)-(c)

**Homework 4** (Due Friday February 23 before the exam): 5.3-1, 5.3-2, 5.3-3, 5.3-4, prove that if a linear optimization problem has 2 optimal solutions then it has infinitely many
optimal solutions.
### Contact Information

- Email: mtait at cmu dot edu
- Office: Wean Hall 7124
- Office hours: Tuesday 2-4 pm or by appointment

### Teaching Assistant

- C.J. Argue
- Email: cargue at andrew dot cmu dot edu
- Office Wean Hall 6207
- Office Hours: Monday afternoon by appointment and Thursday 3-5 pm