Linear Programming
Frequently Asked Questions
Optimization Technology Center of
Northwestern University and Argonne National Laboratory
Posted at http:/www-unix.mcs.anl.gov/otc/Guide/faq/linear-programmingfaq.html
Changes posted to Usenet newsgroup sci.op
Chapter 2
Solving Linear Programs
Companion slides of
Applied Mathematical Programming
by Bradley, Hax, and Magnanti
(Addison-Wesley, 1977)
prepared by
Jos Fernando Oliveira
Maria Antnia Carravilla
A systematic procedure for solving
linear programs the si
CSC445 Linear Programming
Tableau, solvers and degeneracy
George Tzanetakis
University of Victoria
2016
G. Tzanetakis
1 / 30
The Tableau format for Simplex
The Tableau format is a popular way to introduce the simplex
method and closer to how it is usually
MA3231 Linear Programming
W. J. Martin
September 27, 2014
Sample Solutions
LP Assignment 3
1. (Exercise 2.19) Suppose p1 /q1 < p2 /q2 < < pn /qn where the pi and the qi are
sequences of positive real numbers each summing to one. For > 0, the optimal
solut
CSC445 Linear Programming
Introduction
George Tzanetakis
University of Victoria
2016
G. Tzanetakis
1 / 18
Table of Contents I
1 Logistics
2 Plagiarism
3 What is this course about ?
G. Tzanetakis
2 / 18
Course Information
Course outline: https:/heat.csc.uv
CSC445 Linear Programming
The Simplex Algorithm
George Tzanetakis
University of Victoria
2016
G. Tzanetakis
1 / 34
An example
maximize 5x1 + 4x2 + 3x3
subject to 2x1 + 3x2 + x3 5
4x1 + x2 + 2x3 11
3x1 + 4x2 + 2x3 8
x1 , x2 , x3 0
The firt step is to intro
CSC545 Assignment 2. Fall 2016 (50pts)
Student Name:
Instructor George Tzanetakis
Question
1
2
3
4
5
Total
Value
10
30
30
10
10
100
Student Number:
Mark
Overview
The goal of this assignment is to familiarize with degeneracy, efficiency, duality and the us
CSC545 Assignment 1. Fall 2016 (50pts)
Student Name:
Instructor George Tzanetakis
Question
1
2
3
4
5
6
7
Total
1
Value
10
20
10
10
10
20
20
50
Student Number:
Mark
Overview
The goal of this assignment is to familiarize with formulating actual problems as
CSC 445/545: Final exam- Mon. Dec. 7, 1992
The exam is 3 hours long. You should have 6 questions on 8 pages plus 2
blank pages at the end. Closed book. No calculators or other aids permitted.
Question
Marks
1
20
2
20
3
15
1.(a) [10] Convert the following
CSC445/545 Midterm Study Guides, Fall 2016
Tzanetakis, George
Midterm Coverage
Coverage for the first midterm is Chapters 1-4 of the textbook excluding the
section on geometry (2.5 and 3.6)
Chapter 1
Be able to express a problem explained in words as a l
Textbook: Linear Programming, Foundations and Extensions
Robert Vanderbei, Springer
Basic: minimum amount of work for passing the course
Regular: expected amount of work for getting a solid understanding of the material
Advanced: extra work if you are int
CSC 445/545: Midterm Exam
Fall 1992
1.
[25] Apply Phase 1 of the two-phase Simplex method to the following problem to
determine if it is feasible.
Max
x1 x2 x3
subject to
2 x 1 + 5 x 2 + 7 x 3 2
1 x1 2 x2 + 3 x3 3
x1 , x2 , x3
0
2.(a) [5] Write down the
CSC 445/545 Test #2: Fri. Nov. 10, 2000
1.
[25] Find an optimal solution to the transshipment problem where the network, the
shipping costs and the demands are as shown below. You must show all your work
for full marks. Start with arcs (a,e), (b,c) (b, d)
CSC 445/545 Test #1: Fall 2005
1.
I ran the Simplex method on two sample problems using my program and the final
dictionaries are as given below. What (if anything) can you say about the duals of
these two problems?
(a)
[10 marks]
X3
X5
X1
z
(b)
0.83
0.67
Name: _
ID Number: _
CSC 445/545 Test #1
Thurs. Oct. 5, 2006
Instructions:
1.
Put your name on every page of the exam.
2.
No calculators or other aids. Closed book.
3.
You should have seven pages including this header page- the last page is blank.
1
20
2
CSC 445/545 Test #2: Thurs. Nov. 17, 2005
1.
[20] Solve the following transhipment problem starting with the given tree.
Demands are given in the square boxes. The arcs are labeled with the shipping
costs. Show all your work.
Compute prices starting at no
Name: _
ID Number: _
CSC 445/545 Test #2
Monday Nov. 19, 2012
Instructions:
1.
Put your name on every page of the exam.
2.
No calculators or other aids. Closed book.
3.
You should have 8 pages including this header page.
Question
Topic
Max
1
Complementary
Name: _
ID Number: _
CSC 445/545 Test #2
Thurs. Nov. 16, 2006
Instructions:
1.
Put your name on every page of the exam.
2.
No calculators or other aids. Closed book.
3.
You should have eight pages including this header page- the last page is blank.
1
20
2
Name: _
ID Number: _
CSC 445/545 Test #1
Thurs. Oct. 11, 2012
Instructions:
1.
Put your name on every page of the exam.
2.
No calculators or other aids. Closed book.
3.
You should have seven pages including this header page.
Question
Max
1
15
2
25
3
20
4
2-3 Trees
Professor Sin-Min Lee
Contents
Introduction
Introduction
s The 2-3 Trees Rules
s The Advantage of 2-3 Trees
s Searching For an Item in a 2-3 Tree
s Inserting an Item into a 2-3 Tree
s Removing an Item from a 2-3 Tree
Removing
s
INTRODUCTION
What
Li Rui
V00180220
Assignment 1
Question 1
1. It escapes some steps. 2. Message into wet hair, take the bottle, open the bottle, put some shampoo in your hands,
and then put bottle back. After put the shampoo into your hair, and make a lush lather, and then