Optimization Methods in Management Science
MIT 15.053
Recitation 4
TAs: Giacomo Nannicini, Ebrahim Nasrabadi
At the end of this recitation, students should be able to:
1. Interpret the solution and sensitivity report of a problem to take decisions related
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Recitation 10, Friday May 3th, 2013
Problem 1
The Airfare Problem1 . You are trying to get the cheapest airfare that you can. You just
called up and found that the ticket home will cost $4
Optimization Methods in Management Science
MIT 15.053
Recitation 5
TAs: Giacomo Nannicini, Ebrahim Nasrabadi
Problem 1
Suppose we are solving the linear program given in the tableau below:
Basic
( z)
s1
s2
s3
x1
2
5
-3
-2
x2
3
6
-1
0
x3
5
-1
2
2
x4
2
2
-1
Optimization Methods in Management Science
MIT 15.053
Recitation 8
TAs: Giacomo Nannicini, Ebrahim Nasrabadi
At the end of this recitation, students should be able to:
1. Derive Gomory cut from fractional rows of the Simplex tableau.
2. Have an intuititio
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 5, Due: Thursday April 2th, 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Discussing problem sets with other students is permitted. Copyi
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 4, Due: Thursday March 7th, 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Discussing problem sets with other students is permitted. Copyi
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 2 (Second Group of Students)
Students with rst letter of surnames
IZ
Due: February 21 , 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Dis
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 2 (First Group of Students)
Students with rst letter of surnames
AH
Due: February 21 , 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Disc
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 6, Due: Thursday April 11th, 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Discussing problem sets with other students is permitted. Copy
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 1 (Second Group of Students)
Students with rst letter of surnames
GZ
Due: February 12 , 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Dis
Optimization Methods in Management Science
MIT 15.053, Spring 2013
Problem Set 1 (First Group of Students)
Students with rst letter of surnames
AF
Due: February 12 , 2013
Problem Set Rules:
1. Each student should hand in an individual problem set.
2. Disc
Converting a Linear Program to Standard Form
In this tutorial, we briefly explain what standard form is, and how to convert a linear program to standard form
Cleaver, an MIT Beaver
1
Linear Programs in Standard Form
We say that a linear program is in stan
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
15.053 Optimization Methods in Management Science (Spring 2007) Problem Set 5 Due March 22nd, 2007 at 4:30 pm.
You will need 119 points out of 140 to receive a grade of 5.
Problem 1: Weak and Strong Duality (36 Po
15.053
March 13, 2007 Duality 3
There are concepts much more difficult to grasp than duality in linear programming. - Jim Orlin
The concept [of nonduality], often described in English as "nondualism," is extremely hard for the mind to grasp or visualize,
Quotes for today
15.053
February 10, 2011
!
Review of Solving Systems of Equations
!
Any impatient student of mathematics or science
or engineering who is irked by having algebraic
symbolism thrust upon him should try to get
along without it for a week.
I
Quotes of the day
15.053
!
February 8, 2011
You don't understand anything
until you learn it more than one
way.
Marvin Minsky
The Geometry of Linear Programs
the geometry of LPs illustrated
One finds limits by pushing
them.
Herbert Simon
1
What does the
Overview of Lecture
15.053
February 3, 2011
!
Goals
get practice in recognizing and modeling linear
constraints and objectives
More Linear and
Non-linear Programming Models
and non-linear objectives
to see a broader use of models in practice
plus appli
www.ics.uci.edu/./junkyard/
icosahedron-s.jpg
Class website: stellar.mit.edu
Grading and homework policies on website
Announcements on web and by e-mail
No laptops permitted in class, except by permission
!
!
!
Problem Set 1 will be due next Tuesday
ple