ORIE 3300/5300
ASSIGNMENT 4
Fall 2014
Due: 5pm, Wednesday October 1.
Individual work.
Note time change this week.
1. Consider the following tableau for a linear program in standard equality
form:
z
x2
x1
+
+
+
4x3
4x3 + x4
2x3
2x3
3x5
+ 3x5
x5
+ 2x5
2x

ORIE 3300/5300
Homework 2
Fall 2013
Due: 2p, Friday September 20.
This assignment is individual work.
In this assignment, reference is made to linear programs
min cT x
s.t. Ax = b
x0,
(1)
in which A is an m n matrix (m n) and A is of full rank. In this se

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

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

ORIE 3300/5300
Individual work.
ASSIGNMENT 3
Fall 2011
Due: 11am, Tuesday September 20.
1. Next weeks recitation concerns the Diet linear programming model.
In preparation, read pages 2735 in the AMPL book.
2. Below is a picture of the feasible region for

OR&IE 3300/5300 Summer 2009 Exam #2 Wednesday, June 10, 2009 Topics Geometry, sensitivity analysis Closed book exam. Justify all work.
1. Consider the following LP and its optimal tableau. Here x4 and x5 are slack variables for the first and second inequa

ORIE 3300/5300
ASSIGNMENT 1
Fall 2014
Due: 11am, Tuesday, September 9.
This assignment is individual work.
1. Read pages 211 of the AMPL book.
2. The Demo version of AMPL on the AMPL website includes a MODELS
folder containing many useful models. Read thr

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 2015
Prelim #3 Wednesday, June 17, 2015
Topics Duality, Transportation problem
Closed book exam. Justify all work.
1. In the class notes we have considered the following LP.
max
4x1 + 3x2
3x1 + x2
3x1 + 2x2
x1 + x2
x1 0, x2 0
9
1

ORIE 3300/5300
Homework 10
Fall 2013
Due: 2p, Friday November 15
This assignment is individual work.
Dont forget to attach the 2-page coversheet! (Else, lose a point.)
1)
a) On the last page of this assignment is the table from lecture showing all possibl

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

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 3310/5310
Optimization II
Summer 2009
Homework # 1
Due: Monday, July 6 at 2:30 in the OR homework drop box for OR3310. 1. Recall the Farkas Theorem from linear programming: For any m n real matrix A and m -vector b exactly one of the two following sy

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

ORIE 3300/5300
Individual work.
ASSIGNMENT 6
Fall 2008
Due: 3 pm, Friday October 24.
1. A coach must assign four swimmers to a 200-meter medley relay team. He can choose from ve available swimmers, each of whom could swim the 50-meter leg in any

ORIE 3300/5300
ASSIGNMENT 1
Fall 2011
Due: 11am, Tuesday September 6.
This assignment is individual work.
1. Read pages 211 of the AMPL book.
2. The Student Edition of AMPL on the AMPL website includes a MODELS
folder containing many useful models. Read t

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 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 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

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&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
SAMPLE FINAL
2.5 hours
Name:
NetID:
Instructions
1. Print your name and NetID above.
2. Underline your Recitation section above.
3. You may use a basic scientic calculator. No other aids permitted.
4. Answer all questions, explaining your a

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

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

(i)
(ii)
a)
Assignment 6 Question 2
Am=b,mZO
ATyZ 0,bTy<0
We can show that all 4 (in)equalities cannot hold at the same time. In other words, we will
show that if rst 3 of them hold, the 4th one cannot hold.
So lets have such a: and y that
szb, a:>0, and

ORIE 3300/5300
ASSIGNMENT 5
Summer 2017
Solution - Question 2
Solve the following linear program using the revised simplex method.
Introduce slack variables, and use these as the initial basic variables.
maximize 6x1 + 5x2 + 8x3 + 9x4
subject to x1 + x2 +

Assignment 6 Question 4
yxl, x2 and x3 represent the production of economy, standard and luxury cars respectively. x4, x5
and x5 represent the amount of cars of economy, standard and luxury in excess of production levels.
1 2 3 o '1 120 6%;
*_ -1 _ 1 o 0