ISyE 3833 - HW 2
Due Sept 28/29
1. Write the following LP in canonical inequality form (i.e., formulate an equivalent LP that has
canonical inequality form):
min 2x1
s.t.
4x1
2x1
x1
x1
+ x2
+ 3x2
x2
ISyE 3833 - HW 3
Due October 12/13
1. Solve the following LPs using the simplex method. If the LP has an optimal solution, state
it, and state the optimal value. State clearly if the simplex method re
ISyE 3833 - HW 2
Due: Feb 17 / 18
1. Write the following LP in canonical inequality form (i.e., formulate an equivalent LP that has
canonical inequality form):
min 2x1
s.t.
4x1
2x1
x1
x1
+ x2
+ 3x2
x
ISyE 3833 - HW 3
Due October 12/13
Solve the following LPs using the simplex algorithm. If the LP has an optimal solution, state it,
and state the optimal value. State clearly if the simplex method re
Engineering Optimization ISyE 3833 - Quiz 2 - Solution
1. A metallurgy company makes two grades of bronze: high grade and low grade. Both types
of bronze are made by mixing copper and tin. High grade
ISyE 3833: Engineering Optimization
October 4, 2015
Solution Midterm 1 - 2015
Lecturer: Santanu S. Dey
Scribe: Santana, A.
Question 1 My company assembles electronic parts and sells the assembled nal
ISyE 3833: Engineering Optimization
August 27, 2015
Lecture 4
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Blending
Solution:
Variables: As some of the data provided are given in terms of percentage
ISyE 3833: Engineering Optimization
August 27, 2015
Lecture 4
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Blending
Solution:
Variables: As some of the data provided are given in terms of percentage
ISyE 3833: Engineering Optimization
September 1, 2015
Lecture 5
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Transportation
Note that m and n are data, not variables. As well as si , dj and ci,j . T
ISyE 3833: Engineering Optimization
September 3, 2015
Lecture 6
Lecturer: Santanu S. Dey
Scribe: Santana, A.
From now on we will start doing some more complex formulations, for instance, in some
cases
ISyE 3833 - HW 3
Due March 1/2
1. You need to buy a new cell phone now, and are trying to minimize your cell phone costs
for the next 5 years. A new cell phone costs C dollars and lasts for at most 3
ISyE 3833: Engineering Optimization
September 8, 2015
Lecture 7
Lecturer: Santanu S. Dey
Scribe: Santana, A.
In this lecture we do one more linear program formulation and then we move on to
integer fo
ISyE 3833: Engineering Optimization
September 10, 2015
Lecture 8
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Scheduling
Solution:
Variables:
xi : number of nurses beginning on day i, for all i cfw_
ISyE 3833: Engineering Optimization
September 15, 2015
Lecture 9
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
If-Then Constraints
We want to model the following kind of problem.
I need to manufactur
ISyE 3833: Engineering Optimization
August 25, 2015
Lecture 3
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Farmer Joe
Solution:
Variables:
x1 : acres of corn
x2 : acres of wheat
Both variables are c
ISyE 3833: Engineering Optimization
August 25, 2015
Lecture 3
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Farmer Joe
Solution:
Variables:
x1 : acres of corn
x2 : acres of wheat
Both variables are c
ISyE 3833: Engineering Optimization
November 3, 2015
Solution Midterm 2 - 2015
Lecturer: Santanu S. Dey
Scribe: Santana, A.
Question 1 Consider a linear program given in standard form with 2 rows and
Engineering Optimization ISyE 3833 - Quiz 1
Name: W
1. (12 pt) A work uniform manufacturer makes shorts, pants, skirts and jackets. Each
requires labor hours, cloth and trimmings, in the amounts, per
Engineering Optimization ISyE 3833, Spr 2017 - Quiz 4
Name:
Note: In this series of modeling questions, you are asked to write an initial model, and
then to modify it as more information is provided.
ISyE 3833 - HW 2
Due Feb 15/16
1. Write the following LP in canonical inequality form (i.e., formulate an equivalent LP that has
canonical inequality form):
min
s.t.
x1
x1
3x1
x1
x1
2x3
+ x3 =
4
+ 4x
ISyE 3833 - HW 5 - DO NOT SUBMIT - PRACTICE ONLY
1. ISyE is organizing a field trip for n of its students. There are m cabins available, and the
jth cabin has P
capacity Kj , for each j = 1, . . . , m
Nlame: Section: Row:
ISyE 3833: Engineering Optimization
Midterm Exam
October 20th, 2016
_._._
r.
SOLMW 0v:
Remarks.
0 This is a closed book exam.
0 No calculators.
0 There are 4 problems in total
ISYE3133A - Engineering Optimization
Midterm 1 - October 1st, 2012
NAME:
GTID:
SIGNATURE:
Time: 1hr 20 minutes
Instructions:
WORK ALONE. Do not collaborate with anyone.
Show ALL your work.
You will
ISYE3133A - Engineering Optimization
Midterm 1 - February 12nd, 2013
NAME:
GTID:
SIGNATURE:
Time: 1hr 20 minutes
Instructions:
WORK ALONE. Do not collaborate with anyone.
Show ALL your work.
You wi
Problem Set 1
This problem set is meant to be an opportunity for you to review Linear Algebra. Chapter 2 of the
textbook/ hints given here should help you to solve these problems.
1
Summation and For
ISYE3833 - Engineering Optimization
Midterm 1 - September 30th, 2014
NAME:
SECTION:
GTID:
SIGNATURE:
Time: 1hr 20 minutes
Instructions:
WORK ALONE. Do not collaborate with anyone.
Show ALL your work
Problem Set 1 - Solutions
This problem set is meant to be an opportunity for you to review Linear Algebra. Chapter 2 of the
textbook/ hints given here should help you to solve these problems.
1
Summat
ISyE 3833: Engineering Optimization
September 17, 2015
Lecture 10
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Fixed Cost
1.1
An Investment Problem
Solution:
Variables:
xi : equals 1 if production o
ISyE 3833: Engineering Optimization
September 22, 2015
Lecture 11
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
XOR variables
Given
x1 =
1 if decision 1 is taken
0 otherwise
x2 =
1 if decision 2 is t
ISyE 3833 - HW 4
Due November 1/2
1. Consider the following simplex dictionary:
x4
x5
x2 = 1 2x4 +
3x5
x1 = 2 +
x3 = 7 + 5x4 7x5 .
Using the objective function
max z = x2 ,
(a) determine the directio
Name:
Section:
ISyE 3833: Engineering Optimization
Final
December 15, 2016
2:50pm to 5:00pm
Remarks.
This is a closed book exam.
There are 9 problems in total, including one for extra credit.
Write
ISyE 3833 - HW 1
Due: September 6/7
1. (From Winston, Section 2.1, Problem 1) For
1 2 3
A= 4 6 5
8 7 9
find:
1 2
B = 0 1
1 2
and
(a) A,
(f) AB
(b) 3A,
(g) BA
(c) A + 2B
(h) A1
(d) AT
(i) B 1
(e) B T
Engineering Optimization ISyE 3833, Spr 2017 - Quiz 3
Name:
1. (15 points) A factory devoted to making a single product has two production lines.
Line 1 is newer: it requires only 1 unit of labor and
ISyE 3833 - HW 4
Due April 5/6
1. Solve the following LP using the two-phase simplex algorithm. If the LP has an optimal
solution, state it, and state the optimal value. Otherwise, state clearly wheth