OR&IE 3300/5300
Summer 2012
Prelim #2 Monday, June 11, 2012
Topics Geometry of LP, Sensitivity analysis
Closed book exam. Justify all work.
1. Consider the following LP along with a portion of its optimal tableau. Here x5 , x6 , and x7 are slack
variables

OR&IE 3300/5300
Summer 2012
Exam #1 Monday, June 4, 2012
Topics LP formulation, simplex algorithm
Closed book exam. Justify all work.
1. An LP example (maximization) we solved in class involved the following three representations:
(A)
(z)
+
5
3 x2
1
3 x2

Fall 2010
Optimization I (ORIE 3300/5300)
Assignment 4 Solution
Problem 2 (AMPL book 2-3) (a) The AMPL model that minimizes the cost of supply while producing a blend that contains 52 tons of cane sugar, 56 tons of corn sugar, and 59 tons of beet sugar is

PRELIM 4
Closed book exam. Justify all work. 1.
ORIE 3310/5310
April 28, 2009
a. (25 points) You work as an OR analyst for a manufacturing corporation which has production sites i = 1, . . . , m and distribution (sales) centers j = 1, . . . , n . The (int

ORIE 3300: Assignment #1 Solution
Due on Friday, September 13, 2013
1
ORIE 3300 ( ): Assignment #1 Solution
Contents
Problem 1
3
Problem 2
7
Problem 3
8
Problem 4
9
Problem 5
10
Page 2 of 10
ORIE 3300 ( ): Assignment #1 Solution
Problem 1
Part a
The green

1. (a) [2 marks] Dene the term extreme point.
A point x is an extreme point of a convex set C if it does not lie on any open line-segment
in C . Algebraically: there do not exist distinct points y, z C and a number (0, 1)
satisfying x = y + (1 )z .
Now co

ORIE 3300/5300
Individual work.
ASSIGNMENT 6
Fall 2010
Due: 3 pm, Friday October 22.
1. A coach must assign four swimmers to a 200-meter medley relay team. She can choose from ve available swimmers, each of whom could swim the 50-meter leg in any one of t

ORIE 3300/5300
Individual work.
ASSIGNMENT 2
Fall 2008
Due: 3 p.m., Friday September 19.
1. Consider the simple Sudoku-style puzzle below.
4 2
3
You must ll each cell with one of the four numbers 1, 2, 3, or 4. (Four of the cells are already ll

ORIE 3300/5300
Homework 2 Solutions
Fall 2013
1. First, an outline of the solutions:
(a) Recall that J = cfw_j1 , j2 , j3 with j1 < j2 < j3 is basic if the square matrix AJ =
[Aj1 | Aj2 | Aj3 ], which has the j1 th, j2 th, and j3 th columns of A, is inve

OR&IE 3300/5300 Fall 2012
Prelim #1: LP formulation, simplex algorithm Tuesday, 09/25/12
Closed book exam. Justify all work.
1. Consider the following LP along with a portion of its optimal tableau. Here x5 , x6 , and x7 are slack
variables for the rst, s

ORIE 3300/5300
ASSIGNMENT 1
Fall 2008
Due: 3 p.m., Friday September 12. This assignment is individual work.
1. Read pages 111 of the AMPL book. 2. The Student Edition of AMPL on the AMPL website includes a MODELS folder containing many useful mode

OR 3300
Optimization I
Summer 2010
HW 2
Geometry of LP; Sensitivity Analysis
References: Lecture notes; Bradley, Hax and Magnanti chapter 3. Solutions will be posted on Tuesday, June 8. Homework quiz in recitation on Wednesday, June 9.
1. Show that the in

ORIE 3310/5310
Optimization II
Summer 2009
Homework # 3
Due: Monday, July 20, by 2:30p.m., in the OR3310 homework drop box. Print your name clearly on the rst page of your homework.
1. Problem #6, BHM Chapter 8. (catering model) 2. Problem #16, BHM Chapte

OR&IE 3300/5300
Summer 2012
Exam #3 Tuesday, June 19, 2012
Topics Duality, transportation problem
Closed book exam. Justify all work.
1. Suppose that you are given the following simplex tableau:
-z
x1
x2
0
1
0
0
0
1
0
-1
1
For each statement below, give s

OR 3300
Optimization I
Summer 2008
HW 3
LP Duality; Transportation Problem
Due date: Monday, June 16, by 3:20pm in the drop box on 2nd oor Rhodes. References: Lecture notes; Bradley, Hax and Magnanti chapters 4,8. 1. BHM IV/1. 2. BHM IV/2. 3. BHM IV/4, no

PRELIM 1
ORIE 3310/5310
February 19, 2009
Closed book exam. Justify all work. 1. Consider again the the following problem from the homework assignment. The standard decomposition procedure is applied using two subproblems (SUB1, SUB2): ORIGINAL PROBLEM ma

OR&IE 3300/5300 Summer 2009 Exam #1 Monday, June 1, 2009 Topics LP formulation, simplex algorithm Closed book exam. Justify all work.
1. An LP example (maximization) we solved in class involved the following three representations: (A) (-z) +
5 3 x2 1 3 x2

OR & IE 320 Optimization I Summer 2004 Practice Prelim 1 This is a practice prelim. Its goal is to give an idea of the kind of problems that can be asked. It is by no mean a complete collection of all the possible questions that can show up in the p

ORIE 3300/5300
Individual work.
ASSIGNMENT 5
Fall 2008
Due: 3 pm, Friday October 17.
1. Read Chapter 3 in the AMPL book, on transportation and assignment problems, in preparation for next weeks recitations. *Note: for the next few weeks, recitati

ORIE 3310/5310
Optimization II
Summer 2009
Homework # 2
Due: Monday, July 13, by 2:30, in the OR3310 homework drop box.
These rst few problems are practice problems, not to be handed in. Problems 1 and 4 are from the Bradley, Hax, and Magnanti text, while

ORIE 3300/5300
Assignment 6 SOLUTION
Fall 2008
Problem 1 In this problem, we have 5 people (supply) and only 4 stroke styles (demand). Thus, we will need to dene a new stroke style, called bench that everyone can swim in 0 seconds and the person s

OR&IE 3300/5300
Summer 2011
Prelim #3 Wednesday, June 22
Topics Duality, Transportation problem
Closed book exam. Justify all work.
1. In the class notes we have considered the following LP.
max
4x1
3x1
3x1
x1
+ 3x2
+ x2
+ 2x2
+ x2
9
10
4
x1 0, x2 0
All q

OR & IE 320 Optimization I Summer 2004 Prelim 1 Solution
1. (a) The LP that the AMPL model describes is: min s.t 1000
s SU P P LIERS, l LOCS
Shipls costls
l LOCS
Shipls u limits s SUPPLIERS s SU P P LIERS Shipls l limitl l LOCS Shipls 0

Announcements
recitation 1
Posted on: Sunday, August 28, 2016 7:57:42 PM EDT
Before the first recitation, browse the first
chapter of the AMPL textbook. Exercise 1-4 (i.e., 4th exercise
of first chapter) is the focus of the recitation.
The first recitatio

Recall the example for the high school simplex method:
min
s.t.
x1
x1
x1
x1
x1
x2
+
2x2
2x2
x2
,
+
,
x3
x3
+
,
x4
x4
+
,
x5
x5
=
=
=
2
4
2
0
Begin by rearranging as follows:
min
s.t.
x3
x4
x5
x
=
=
=
2
4
2
0
current
basic variables:
current
basic solution

Recall the following iterations we recently performed using the simplex method,
to solve linear program that has served as our primary example:
min
s.t. x3
x4
x5
x
x1
x1
x1
x1
= 2
= 4
= 2
0
min cT x
s.t. Ax = b
x 0
x2
2x2
+ 2x2
x1 enters, x5 blocks
min
s.