American
University of Beirut
ENMG 604
Assignment 3
Ziad Saliba
200601485
Problem 1:
a) If the optimal tableau shows one or more nonbasic variables with zero coefficients in Row 0,
then there are alternative optimal solutions. So, in order for the curren
Homework #2 Solution
Chapter 3 Linear Programming Methods
1.
Consider the following linear program.
Maximize z = 5x1 + 3x2
subject to
3x1 + 5x2 15
5x1 + 2x2 10
x1 + x2 2
x2 2.5
x1 0, x2 0
a. Show the equality form of the model.
b. Sketch the graph of the
Homework #3 Solution
Problem
L
2. (20 points) In thc simplex tableau tbr a ma,riui4glrox problem given in the table
below, the values of the five constants
p,
f u" unknown (assume there are
pzt
a,1t
u2t
fcfw_
X4
.I;
Xa
no artifi cial variables):
Basis
lx
American University of Beirut
Faculty of Engineering and Architecture
Engineering Management Program
ENMG 604: Deterministic Optimization  Spring 2010
Midterm Exam
Instnrctor: Prof.
St'dent
Narne: e Olru[i
7
Ali A. Yassine
Apr. 14,2010;45:30 pm
O^
Yo
ENMG 604 TakeHome, MidTerm
Examination
Solve as many of the following problems as you
can. Grades will be normalized around the
average score for the whole class.
1. Solve the following LP using algebraic arguments, i.e., without using a
solver and with
Selecting Telecommunication Carriers to Obtain
Volume Discounts
Prepared by:
Maya Itani
Hani Zein
Supervised by:
Prof. Khalil Hindi
Course # ENMG 604
Engineering Management Program
Faculty of Engineering and Architecture
Table of Contents
1Introduction
2
AmericanUniversityofBeirutFacultyofEngineeringandArchitecture
EngineeringManagementProgram
Fall2008ENMG604:DeterministicOptimization
Prof.A.Yassine
HomeworkSet#4
Problem 1:
In intermodal transportation, loaded truck trailers are shipped between railroad
2009
American University of Beirut
Engineering
Management
Program
ENMG 604
Deterministic
Models
Term Paper
optimization
[ ManHour Optimization Model for
Design Consulting Projects]
Group Members:
Malak Hamdan
Moutafa Fattal
Youmn El Rawi
Tarek Atoui
Intr
E
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
F GH I
J
K
item y widtheight
x
h
text
PurchaseBox
L
init/result
# 265 TreePlan Tryout
555
Thank you for trying TreePlan.
55
#
This is a fully functional, try
American
University of Beirut
ENMG 604
Assignment 2
Ziad Saliba
200601485
Exercise 3.20
a) The basic solution is:
X = (X1, X2, X3, X4, X5, X6, X7) = (9, 0, 4, 0, 0, 15, 0) with Z = 22
b) If x5 were to enter the basis, then one of the basic variables x1, x
Problem 1:
The following network represents the problem at hand:
XP = Peak of mount X where X = W, J, P
XB = Base of mount X where X = W, J, P
The problem is to find the maximum hiking distance given the constraints that no mountain is to
be climbed for t
QUESTION 11:
From the sketch attached, we can see that the objective function z coincides with C2. This is evident from the
fact that z is parallel to C2. This means that there are an infinite set of optimal solutions that maximizes z while
satisfying all
The Shortest Path Problem
The shortest path problem appears either directly, or as a subsidiary problem, in
many applications: e.g., vehicle routing problems; some problems of investment and
of stock control; many problems of dynamic programming with disc
The Simplex Method of Linear Programming
1
A Motivating Example
consider:
max 5x1
s.t. 2x1
4x1
3x1
+4x2
+3x2
+ x2
+4x2
+3x3
+ x3
+2x3
+2x3
xi
5
11
8
0 i
(1)
For every choice of the decision variables x1 , x2 and x3 , dene slack variables
x4 , x5 , x6 an
The Transshipment Problem
1
Introduction
In the transshipment problem, also called the minimum cost network ow problem,
a uniform product, available in known quantities at each of a number of sources, is
to be shipped to a number of destinations, each wit
Correction of the midterm:
Problem 1: correct but done with a different explanation 3/3
Problem 2: correct but done with a different explanation 3/3
Problem 3: correct but done with a different explanation 3/3
Problem 4: correct full grade 3/3
Problem 5:c
Optimizing Highway
Transportation at the United
States Postal Service
ENMG 604
Presented to: Dr. Khalil Hindi
Done by: Joury Younes
Introduction
Problem
The United States Postal Service, also known as USPS, is
an independent United States government agenc
Problem 3.20:
(a) The basic solution described by the above tableau is:
X = (X1, X2, X3, X4, X5, X6, X7) = (9, 0, 4, 0, 0, 15, 0) with Z = 22
(b)
The entering variable is specified to be X5
The leaving variable is to be determined using the Minimum Ratio
Moustafa Fattal
2009
200502926
ENMG 604
March
31,
Assignment 3
Problem 1:
a) If the optimal tableau shows one or more nonbasic variables with zero coefficients in Row 0,
then there are alternative optimal solutions. So, in order for the current solution
Problem 1:
The initial set of permanently connected nodes contains both LA & CH. This is because this link
is a must in order accommodate the expected heavy traffic. Therefore, the initial total length is
2000 miles. Other nodes are chosen as per the mini
Problem 2:
The objective is to maximize the total return:
The constraints are as follows:
No more than 2 projects can be selected in any year:
Total investment in any year cannot exceed 9:
Project B must be selected after project A:
Project A and B canno
Sensitivity and Duality in Linear Programming
Parameters in LP models (such as costs, prots, yields, consumption rates, supplies and demands) are almost never known with certainty at the time the model
is built and solved. Therefore, nding the mathematica
Rani Kurban
ENMG 656
Assignment: 3
HP Merced decision case:
Goal:

The goal of HP was to produce scalable high performance computing to run complex
applications for businesses.
The options of HP:

HP would join Suns Solaris campaign standardizing UNIX p