ESE304 - Introduction to Optimization (Exam #1)
Fall Semester, 2013
M. Carchidi
Problem #1 (20 points) - An Empty Feasible Region
Given the following LP
max z = 2x1 + x2 + x3
s.t.
x1 + x2 + x3 50
x1 + 2x2 + 3x3 180
x1 , x2 , x3 0
(Objective Function)
(Con

ESE304 - Introduction to Optimization (Homework #4) Fall Semester, 2010 M. Carchidi Problem #1 (20 points) ToyWorld makes soldiers (x1 ), trains (x2 ) and dolls (x3 ) and the LP for maximizing ToyWorlds monthly prot (in dollars) is as follows. max z = $20

ESE304 - Introduction to Optimization (Homework #2) Fall Semester, 2010 M. Carchidi Problem #1 (15 points) Use the simplex method to solve the following LP. max z = 2x1 x2 + x3 st 3x1 + x2 + x3 60 x1 x2 + 2x3 10 x1 + x2 x3 20 x1 , x2 , x3 0 (Objective Fun

ESE304 - Introduction to Optimization (Exam #2)
Spring Semester, 2011
M. Carchidi
Useful Information
Starting with the following LP,
max z = cT xB + cT xN
(Objective Function)
B
N
s.t.
AB xB + AN xN = b (Constraints with b 0)
xB , xN 0
(Sign Restrictions)

ESE304 - Introduction to Optimization (Homework #6) Fall Semester, 2010 M. Carchidi Problem #1 (20 points) A river runs along the curve described in the xy plane by the equation y = 2x2 + 19. A sherman is driving along a straight road described in the xy

ESE304 - Introduction to Optimization (Exam #2)
Spring Semester, 2008
M. Carchidi
Problem #1 (25 points)
The Giapetto LP problem (without the x1 40 constraint) that we have
been studying in class is given by
max z = $3x1 + $2x2
s.t.
2x1 + x2 100
x1 + x2 8

ESE304 - Introduction to Optimization (Homework #5)
Spring Semester, 2010
M. Carchidi
Problem #1 (15 points)
Determine the optimal solution to the following MIP problem.
max
s.t.
z = 2x1 + x2
(Objective Function)
7x1 + 3x2 34
(Constraint #1)
14x1 + 9x2 79

ESE304 - Introduction to Optimization (Practice Problems)
Fall Semester, 2007
M. Carchidi
Problem #1 - Chapter 12
A box has dimensions x by y by z . The top of the box (having dimensions
x by y ) is opened. Determine the values of x, y and z if the surfac

ESE304 - Introduction to Optimization (Homework #5)
Fall Semester, 2009
M. Carchidi
Problem #1 (15 points)
Determine the optimal solution to the following MIP problem.
max
s.t.
z = 2x1 + x2
(Objective Function)
7x1 + 3x2 34
(Constraint #1)
14x1 + 9x2 79
(

Notes For Optimization Theory &
Analysis
(ESE 304)
Michael A. Carchidi
October 15, 2009
Chapter 4 - The Simplex Algorithm and Goal Programming
The following notes are based on the text entitled: Operations Research by
Wayne L. Winston (4th edition), and t

University Of Pennsylvania Department of Electrical and Systems Engineering ESE304 Optimization Theory & Analysis (Course Outline) Instructor: Dr. Michael A. Carchidi -Textbook: 1.) Operations Research by Wayne L. Winston (Required) (Thomson, Brooks/Cole,

ESE304 - Introduction to Optimization (Homework #2)
Spring Semester, 2009
M. Carchidi
Problem #1 (10 points)
Consider a feasible region described by
3x1 + x2 30
,
2x1 + x2 25
,
x1 , x2 0
Show that it is bounded and then determine all its extreme points (b

ESE304 - Introduction to Optimization (Homework #5)
Spring Semester, 2009
M. Carchidi
Problem #1 (15 points)
Determine the optimal solution to the following MIP problem.
max
s.t.
z = 2x1 + x2
(Objective Function)
7x1 + 3x2 34
(Constraint #1)
14x1 + 9x2 79

ESE304 - Introduction to Optimization (Homework #5) Fall Semester, 2010 M. Carchidi Problem #1 (15 points) Determine the optimal solution to the following MIP problem. max s.t. z = 2x1 + x2 (Objective Function)
7x1 + 3x2 34 (Constraint #1) 14x1 + 9x2 79 (

ESE304 - Introduction to Optimization (Homework #4)
Spring Semester, 2011
M. Carchidi
Problem #1 (15 points)
Determine the optimal solution to the following MIP problem.
max
s.t.
z = 2x1 + x2
(Objective Function)
7x1 + 3x2 34
(Constraint #1)
14x1 + 9x2 79

ESE304 - Introduction to Optimization (Homework #3)
Fall Semester, 2009
M. Carchidi
Problem #1 (30 points)
Consider the Dorian Auto problem (Example #2 in Chapter 3 of the text).
a.) (5 points) Find the range of values on the cost of a comedy ad for which

ESE304 - Introduction to Optimization (Homework #3) Fall Semester, 2010 M. Carchidi Problem #1 (30 points) Consider the Dorian Auto problem (Example #2 in Chapter 3 of the text). a.) (5 points) Find the range of values on the cost of a comedy ad for which

ESE304 - Introduction to Optimization (Exam #1)
Spring Semester, 2011
M. Carchidi
Problem #1 (30 points)
National Disc Corporation manufactures the discs used in producing DVDs
and Blu-Ray discs. Their local plant run 24 hours a day, 7 days a week. On
a g

ESE304 - Introduction to Optimization (Exam #2)
Spring Semester, 2014
M. Carchidi
Useful Information
Starting with the following LP,
max z = cT xB + cT xN
(Objective Function)
B
N
s.t.
AB xB + AN xN = b (Constraints with b 0)
xB , xN 0
(Sign Restrictions)

ESE304 - Introduction to Optimization (Exam #1)
Fall Semester, 2011
M. Carchidi
Problem #1 (20 points)
Suppose that the following tableau is encountered during the nth iteration
of the Simplex Method while solving a maximization problem.
Row
0
1
2
3
4
z x

ESE304 - Introduction to Optimization (Exam #1)
Fall Semester, 2007
M. Carchidi
Instructions:
1.) You must do all six (6) of the following problems.
2.) This exam is open book and open notes.
3.) You may use a calculator, but no laptop computers.
4.) Plea

ESE304 - Introduction to Optimization (Exam #1)
Spring Semester, 2008
M. Carchidi
Problem #1 (25 points)
All steel manufactured by Steelco must meet the following requirements: It
must contain: (a) between 3.2% - 3.5% carbon, (b) between 1.8% - 2.5%
silic

Notes For Optimization Theory &
Analysis
(ESE 304)
Michael A. Carchidi
April 2, 2014
Chapter 6 - Sensitivity Analysis and Duality
The following notes are based on the text entitled: Operations Research by
Wayne L. Winston (4th edition), and these can be v

ESE304 - Introduction to Optimization (Exam #1)
Fall Semester, 2006
M. Carchidi
Instructions:
1.) You must do all six (6) of the following problems.
2.) This exam is open book and open notes.
3.) You may use a calculator, but no laptop computers.
4.) Plea

Lecture Notes For Optimization Theory
& Analysis
(ESE 304)
Michael A. Carchidi
November 17, 2009
Chapter 9 - Integer Programming
The following notes are based on the text entitled: Introduction to Mathematical Programming by Wayne L. Winston and Munirpall

Notes For Optimization Theory &
Analysis
(ESE 304)
Michael A. Carchidi
October 15, 2009
Chapter 5 - Sensitivity Analysis: An Applied Approach
The following notes are based on the text entitled: Operations Research by
Wayne L. Winston (4th edition), and th

Notes For Optimization Theory &
Analysis
(ESE304)
Michael A. Carchidi
September 15, 2009
Chapter 3 - Introduction to Linear Programming
The following notes are based on the text entitled: Operations Research by
Wayne L. Winston (4th edition), and these ca

Notes For Optimization Theory &
Analysis
(ESE304)
Michael A. Carchidi
September 15, 2009
Chapter 2 - The Algebra of Scalars, Matrices and Vectors
The following notes are based on the text entitled: Operations Research by
Wayne L. Winston (4th edition), an

ESE304 - Introduction to Optimization (Exam #1)
Spring Semester, 2009
M. Carchidi
Problem #1 (25 points)
Furnco manufactures tables and chairs. Each table and chair must be made
entirely out of oak or entirely out of pine. A total of 150 board feet of oak

36-617: Applied Linear Models
Fall 2016
HW4 Solutions
Due: 10/5/2016
Readings through 9/28/2016: Sheather Ch. 2 and 3
Readings for next week: Sheather Ch. 5 and 6
This assignment contains 4 questions. There are 91 total points. Partial credit will be give

ESE304 - Introduction to Optimization (Homework #2)
Spring Semester, 2012
M. Carchidi
Problem #1 (15 points)
The simplex method is a typically ecient algorithm for solving linear programming problems. However, thers is no version of it that has been shown

ESE304 - Introduction to Optimization (Homework #4)
Spring Semester, 2012
M. Carchidi
Problem #1 (20 points)
ToyWorld makes soldiers (x1 ), trains (x2 ) and dolls (x3 ) and the LP for
maximizing ToyWorlds monthly profit (in dollars) is as follows.
max z =

ESE304 - Introduction to Optimization (Homework #4)
Spring Semester, 2012
M. Carchidi
Problem #1 (20 points)
A river runs along the curve described in the xy plane by the equation
y = 2x2 + 19. A fisherman is driving along a straight road described in
the

ESE304 - Introduction to Optimization (Homework #5)
Spring Semester, 2012
M. Carchidi
Problem #1 (20 points)
A hiker wants to go on a short hike and he must decide what to carry. His
choices are to carry: Food, Water, Eating Utensils, a Compass and a Map.