Problem 3
Recall the following standard linear programming form described in lecture:
min cx
st
Ax > b
x>0
Convert the following linear program to this form:
max 3q + 6r 7s
st
q + 2r > -4
2.5 q - r > 7
q + r = -4
q>0
s>0
Specifically, write out the formul

IOE 310: Introduction to Optimization
Homework 3
Information:
Homework 3 is due Wednesday January 27, 2016 by 9am. No late assignments will be
accepted.
Homework must be uploaded to Canvas.
Students may work together, but should each write up their own so

IOE 310 Lab #1 Fall 2015
Problem 1
a) Consider the following LP formulation:
maximize
x+2 y
subject to
3 x+5 y 24
x+ y 7
x , y 0
Which of the following are feasible solutions (x,y)? What is the objective value for these solutions?
(-1,1) This is not a fea

IOE 310: Introduction to Optimization
Homework 2
Information:
Homework 2 is due Wednesday January 20, 2016 by 9am. No late assignments will be
accepted.
Homework must be uploaded to Canvas.
Students may work together, but should each write up their own so

IOE310 Fall 2015
Problem Set 3
Information:
Problem set 3 is due Wednesday September 30, 2015 by 9am. No late assignments
will be accepted.
Homework must be uploaded to CTools.
This homework assignment must be typed. Hand-written homework will not be
grad

IOE 310
1
Problem Set 3
Fall 2015
Solution
What is one of your favorite ways to spend a free hour or two when you get time to relax?
I enjoy going to hot vinyasa yoga at Center for Yoga - it also helps me get super zen for exams!
2
Solution
Under what con

IOE310 Fall 2015: Solution
Problem Set 2
Information:
Problem set 2 is due Wednesday September 23, 2015 by 9am. No late assignments
will be accepted.
Homework must be uploaded to CTools.
This homework assignment must be typed. Hand-written homework will n

IOE 310
1
Problem Set 5 Solution
Fall 2015
Solution
What is one of your favorite restaurants in Ann Arbor?
Rich J.C. on South U - I love Korean food!
2
Solution
Are you allowed to bring a cheat sheet to the exam? If yes, what size and what can it contain?

IOE310 Fall 2015
Problem Set 12
Information:
Problem Set 12 is due Monday December 14, 2015 by 9am. No late assignments
will be accepted.
Homework must be uploaded to Canvas. It can be hand-written and scanned.
Students may work together, but should each

IOE 310 Homework Number 5 Due: October 16, 2007 1. Consider the Linear Programming Problem: Min z = x1 2x1 x1 x1 0 + + + x2 3x2 3x2 x2 0 + + + 2x3 x3 3x3 x3 0 7 3
(a) Using the formulas derived in class, derive the tableau associated with the b

IOE 310 Winter 2007 Final Exam
April 13, 2007
Name: Instructions This is a closed book, closed notes exam. You may use one double sided 8 11 inch note sheet and calculator during the exam. Note that not all problems carry the same weight. There

IOE310 Midterm Exam February 21, 2007
Name:_
Instructions This is a closed book, closed notes exam. You may use one double sided 8-by-11 "note sheet" and calculator during the exam. There are four problems in the exam and 12 pages (including t

To. nun-n 12y: lab?!
6
IOESIO Fall 2015
Problem Set 10
Information:
Problem Set 10 is due Friday December 4, 2015 by 5pm. No late assignments will
be accepted.
Homework must be uploaded to Canvas. It can be band~written and scanned.
Students may work toge

1. Title: Carton-Mix Optimization for Walmart.com Distribution Centers
Authors: Sanjay L. Ahire, Manoj K. Malhotra, John B. Jensen
Volume: 45 Issue 4
Page Range: 341 - 357
Due to a considerable increase in online shopping at Walmart, many distribution
cen

Problem 1
Sets
P-set of people Arjun could tell the secret to
C-set of circles at the University
Parameter
apc -whether or not person p has affiliation with circle c, p P, c C (1=yes, 0=no)
Variable
xp whether or not Arjun tells person p the secret, p P (

IOE310
Review Questions on the Simplex Method
The Steps of the Simplex Method
1) Find an initial basic feasible solution (BFS) by introducing artificial variables as
needed
2) Compute the reduced cost of each non-basic variable
3) If all reduced costs are

IOE 310: Assignment #11
Due on Wednesday 12/09/2015
Prof. A. Cohn
Problem 1
Where will you spend winter break?
Solution:
Florida and Puerto Rico.
Problem 2
Consider the linear program:
Min 4x + 2y z
St x + y + z 5
2x z 10
x, y, z 0
a) Construct the dual y

IOE310: Introduction
to Optimization
Monday, September 14, 2015
The Game: Scheduling Residents in the
Pediatric Emergency Department
Professor Amy Cohn
1
Announcements
Labs start on Thu. Sept. 17
Changing
labs
First problem set is posted to the class web

IOE310: Introduction
to Optimization
Wednesday, September 16, 2015
LP Models, Standard Forms, and Notation
Jeremy Castaing, IOE Doctoral Student
1
Announcements
Problem Set 1 was due this morning at 9am
Problem Set 2 has been posted and is due next
Wednes

IOE310: Introduction
to Optimization
Wednesday, September 23, 2015
Binary Programs
Professor Amy Cohn
1
Announcements
Problem Set 2 was posted at 9am this morning Wednesday
Lab 1 is due on Thursday at 9am
Reminder:
You
must go to your assigned lab
You m

IOE310 Fall 2015
Problem Set 11
Information:
Problem Set 11 is due Wednesday December 9, 2015 by 9am. No late assignments
will be accepted.
Homework must be uploaded to Canvas. It can be hand-written and scanned.
Students may work together, but should eac

IOE 310
1
Problem Set 6 Solution
Fall 2015
Solution
Will you see the new Star Wars movie when it comes out? On the rst day? Couldnt care less?
Denitely!
2
Solution
What should you do if you think there was an error in grading your mid-term exam?
You have

IOE310: Introduction
to Optimization
Wednesday, September 16, 2015
LP Models, Standard Forms, and Notation
Jeremy Castaing, IOE Doctoral Student
1
Announcements
Problem Set 1 was due this morning at 9am
Problem Set 2 has been posted and is due next
Wednes

IOE310
Review Questions on the Simplex Method
Solutions
The Steps of the Simplex Method
1) Find an initial basic feasible solution (BFS) by introducing artificial variables as
needed
2) Compute the reduced cost of each non-basic variable
3) If all reduced

IOE310 Fall 2015
Exam 2 Solution
November 18, 2015
Instructions
Be sure to PRINT your name in addition to signing the honor pledge.
Show all work and write legibly.
Write the Honor Pledge ("I have neither given nor received aid on this
examination.") at t

IOE 310Fall 2015
Lab #2 Solution
Problem 1
Goofy Technologies has three new versions of its flagship laptop computer coming out this fall:
the Kermit, the Muppet, and the Homer Pro. However, reach of these models requires a slightly
different manufacturin

IOE310 Fall 2011
Problem Set 4
Solutions to Q 11
Problem 11
a) Suppose that you are trying to build teams for intramural soccer. You have a set S of
soccer players to assign to t teams, each with n players. There is a set P of positions to fill
for each t

Problem 1
From
To # Units Shipped
Upper Bound
Lower Bound Cost
SF
Portland
25
25
0
1.50
SF Salt Lake City
55
90
0
3.50
SF
Lincoln
0
10
0
1.25
SF
Dallas
20
80
0
3.00
SF
Atlanta
0
10
0
2.50
SF
Miami
0
30
0
2.80
ChicagoSalt Lake City
65
100
0
6.00
Chicago
Li

IOE 310 Fall 2011
PS4 Solution
Problem - 6.
a) Variables:
xF
xN
xM
xL
number
number
number
number
of
of
of
of
Fiction books.
Non-fiction books.
Magazines.
Large-print titles.
Objective:
maximize xF + 0.5xN + 0.2xM + 0.25xL
(1)
Constraints:
xF + 2xN + 0.25