Math 354: Section H6, Summer 2004 (01:640:354:H6:83504)
Linear Optimization


July 12 - August 17
Mondays, Tuesdays, Thursdays, 6:15-8:45 in Scott Hall 206

Official course description:

Linear programming problems, the simplex method, duality theory, sensitivity analysis, introduction to integer programming, the transportation problem, network flows, and other applications.
Prerequisite: Linear Algebra, 640:250.

My information:

Text:

Kolman and Beck, Elementary Linear Programming with Applications, 2nd ed., Academic press, 1995.

Grades:

We will have homework, quizzes, two midterm exams, and a cumulative final exam.

Late homework and make-up quizzes will not be accepted or given without a good excuse.

The grades break down as follows:

Homework30%
Quizzes15%
Midterm #115%
Midterm #215%
Final Exam25%

Schedule:

LectureDateSectionsTopics
1Mon 7/121.1,0.1-0.3 Introduction to Linear Programming, brief review of Linear Algebra
2Tue 7/130.4,0.5,1.2,1.3 Brief review of Linear Algebra (continued), matrix notation for Linear Programming problems, geometry of Linear Programming problems
Quiz #1: pdf or LaTeX
Solutions to Quiz #1: pdf or LaTeX
3Thur 7/151.4,1.5 The Extreme Point Theorem, basic solutions
Homework #1 (pdf or TeX) due
Solutions to Homework #1: pdf or LaTeX
4Mon 7/192.1 The Simplex Method
Nice examples of the Simplex Method
Here are examples that are even more fun!
Homework #2 (pdf or LaTeX) due
Solutions to Homework #2: pdf or LaTeX
5Tue 7/202.2,2.3 a little bit of Degeneracy and cycling, artificial variables
Quiz #2 (covering convexity and the Extreme Point Theorem, guaranteed to be proof-free): pdf or LaTeX
Solutions to Quiz #2: pdf or LaTeX
6Thur 7/22Catch up and review
Homework #3 (pdf or LaTeX) due
Solutions to Homework #3: pdf or LaTeX
7Mon 7/26 Midterm #1: pdf or LaTeX
Midterm #1 solutions: pdf or LaTeX
Midterm #1 review problems: pdf or LaTeX
Solutions to above review problems: pdf or LaTeX
(Thanks to Drew Sills for letting me steal these problems from his midterm.)
8Tue 7/273.1,3.2 Duality and the Duality Theorem
9Thur 7/293.3,3.4 the Dual Simplex Method
In-class not-to-be-turned-in problem: pdf or LaTeX
Solution to the above: pdf or LaTeX
Homework #4 (pdf or LaTeX) due
Solutions to Homework #4: pdf or LaTeX
10Mon 8/23.5,3.6,4.1 The Revised Simplex Method, Sensitivity Analysis, introduction to Integer Programming
Homework #5 (pdf or LaTeX) due
Solutions to Homework #5: pdf or LaTeX
11Tue 8/34.2,4.3 Cutting Plane Methods, Branch and Bound Methods
Quiz #3: pdf or LaTeX
Solutions to Quiz #3: pdf or LaTeX
12Thur 8/5 Catch up and review
Homework #6 due: turn in solutions to problems 5, 7, and 8 from the Midterm #2 review problems below
13Mon 8/9 Midterm #2: pdf or LaTeX
Midterm #2 solutions: pdf or LaTeX
Midterm #2 review problems: pdf or LaTeX
Solutions to above review problems: pdf or LaTeX
14Tue 8/105.3,5.4 graphs and networks, the Maximal Flow Problem
Description of the Ford-Fulkerson Algorithm with nice examples in Java
Handout explaining the Ford-Fulkerson Algorithm: pdf or LaTeX
15Thur 8/125.1,5.2,5.5 The Shortest Route Problem, the Transportation Problem, the Assignment Problem
Quiz #4: pdf or LaTeX
Solutions to Quiz #4: pdf or LaTeX
16Mon 8/16 Review
Homework #7 (pdf or LaTeX) due
Solutions to Homework #7: pdf or LaTeX
17Tue 8/17 (Cumulative) Final Exam
Final Exam review problems: pdf or LaTeX
Solutions to the above problems: pdf or LaTeX

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