Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2015)
Homework 4
Due: Friday, Sep 25th
Question 1. The manager of a computer help center needs to determine a shift schedule for his staff. The
IEOR 162: PROBLEM SET 4
DUE OCT 2
For this problem set, please submit an electronic copy of your solutions. In this problem
set, you will set up four spreadsheets. One spreadsheet for each problem. Please set up
the all the spreadsheets in one Excel le. F
IEOR 162 Final Exam Problem (Sensitivity Analysis)
Seung Hun Ham (20957715)
Question
Berkeley Investment decided to invest $100 in a bond and a stock. They found that the bond yields 10% interest
rate and the stock yields 20% dividend yield. They also fou
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2015)
Homework 2
Due: Friday, Sep 11th
Question 1. An investor has money-making activities A and B available each year for the next 5 years.
Ea
Davis Ng
IEOR 162
Exam Problem: Revised Simplex Algorithm
Maximize: 2X1+X2+X3
Such That:
2X1+X3<= 50
X1+2X2+X3<=60
X3+X2 <=40
X1,X2,X3 >=0
Solution:
Rewritten in standard form:
X1=25 X2=17.5 S3=22.5 max is 67.5
Maximize: 2X1+X2+X3
Such That:
2X1+X3+S1= 50
Solution to IEOR 162 Midterm Fall 2007 (30 points total for any three questions)
1. The optimal solution is found to be z = 12, x1 = 0, x2 = 6.
Grading: Feasible region (5) Isoprofit line (3) Unique solution (2) 2. Let x1 = Units of Process 1.
x2 = Units
IEOR 162, Spring 2011
Suggested Solution to Sample Midterm 1
1. (a) The graphical solution is shown in the gure below. The feasible region is the shaded
zone. The dashed line is the isoprot line, and the arrow is the improving direction. The
problem is un
IEOR 165 Spring 2004 Final Exam May 19, 2004 5.00 - 8.00 pm 2 Leconte Q1. A random sample of size 10 is taken from population X. Suppose the sample mean is 102 and the sample variance is 121. Also a random sample of size 15 is taken from population Y. For
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2015)
Homework 5
Due: Friday, October 2nd
Question 1. A company can make a product in three sizes - large, medium, and small - that yield a net
IEOR 162, Fall 2011
Homework 10
1. (Problem 9.2.10; 5 points) If x and y are integers, how could you ensure that at least one of x + y 3
and 2x + 5y 12 is satised?
2. (Problem 9.2.11; 5 points) If x and y are integers, how could you ensure that whenever x
Department of Industrial Engineering & Operations Research
IEOR162 Linear Programming
Exam 1 03/19/2003
Name:
Grade:
1. (20 points) Draw the feasible region of problem (P). Illustrate two isoprot lines and show the direction of improvement in the objectiv
IEOR 162, Fall 2011
Homework 01
1. (Modied from Problem 3.2.3; 10 points) Leary Chemical manufactures three chemicals: A, B, and
C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an
hour costs $4 and yields 3 uni
UNIVERSITY OF CALIFORNIA Industrial Engineering and Operations Research
Midterm Exam Spring 2002
LINEAR PROGRAMMING IEOR162 Professor Dorit Hochbaum
Attempt all five questions. Show all your work. If you feel you need more space use the back of the preced
IEOR 162, Fall 2011
Homework 08
Note. If an LP has n variables and m constraints (excluding nonnegativity constraints), its dual LP MUST
have n constraints (excluding nonnegativity constraints) and m variables.
1. (Modied from Problem 6.3.6; 20 points) Su
IEOR 162 Linear Programming Spring 2007
Discussion Section Handout 3
Some modeling problems: 1. It's Monday and you have $200. You're objective is to maximize the amount of money you have on Friday. Each day of the week, you can choose to invest any
IEOR 162, Fall 2011
Homework 07
1. (Modied from Problem 6.1.4; 17 points) Consider the Dorian Auto problem as below:1
Dorian Auto manufactures luxury cars and trucks. The company believes that its most
likely customers are high-income women and men. To re
Department of Industrial Engineering & Operations Research
IEOR162 Linear Programming
SAMPLE Midterm Exam 1
Fall 2011
Name: SAMPLE Midterm Exam 1
Grade: SAMPLE Midterm Exam 1
1. Consider the following linear program
max 3x1 2x2
s.t. x1 x2 5
2x1 x2 4
x2 4.
IEOR 162, Fall 2011
Homework 11
1. (10 points) Four jobs must be processed on a single machine. The hours required to perform each job
and the due time (in hours) for each job are shown in the table below. Use the branch-and-bound
method to determine the
Timmy Siauw, Alexandre Bayen
An Introduction to MATLAB Programming
and Numerical Methods for Engineers
January 16, 2013
Foreword
This book includes the material taught at UC Berkeley in the class E7, Introduction to computer programming
for scientists and
Engineering 7:
Introduction to Programming for Engineers
Prof. Alexandre Bayen
Spring 2011
Final Examination
May 10, 2011
75 Questions, 170 minutes
Notes:
1. Before you begin, please check that your exam has 28 pages (including this one).
2. Write your na
IEOR 221 - Spring 2013
Homework 11
Due 05/09/2013
1. Consider a Binomial Lattice model with the following parameters:
Number of periods: n = 4;
Current stock price: S = 300;
Up factor: u = 1.1224;
Down factor: d = 0.8909;
Interest rate per period: 0.
IEOR221-Spring 2013
Practice Questions
1. Given six stocks A, B, C, D, E and F with the following data:
Stock Expected Return (%) Variance (%)
A
8
4
B
10
9
C
12
16
D
14
25
E
16
36
F
18
49
It is also given that the covariance between any of the two stocks
Final Exam Solutions
1) c
2) c
3) b
4) b
5) c
6) c
7) c
8) a
9) b
10) b
11) b
12) a
13) c
14) c
15) c
16) a
17) a
18) d
19) d
20) c
21) b
22) b
23) c
24) b
25) b
26) b
27) b
28) a
29) d
30) e
31) c
32) a
33) c
34) d
35) c
36) d
37) a
38) d
39) c
40) a
41)
UNIVERSITY OF CALIFORNIA
COLLEGE OF ENGINEERING
E7: INTRODUCTION TO COMPUTER PROGRAMMING
FOR SCIENTISTS AND ENGINEERS
Professor Raja Sengupta
Spring 2010
Final ExamMay 11, 2010
[85 points ~ 3 hours]
Question
Points
Question
Points
Part I
5
Part VII
5
Part
E7 Sample Questions Solutions
Angela, Gerd, Nate, and Toby
May 10, 2013
NOTE: These sample questions are meant to give you a taste of what you could encounter in the nal.
Solving these questions does NOT give you a complete feedback for your exam preparat
E7 Sample Questions
Angela, Gerd, Nate, and Toby
May 8, 2013
NOTE: These sample questions are meant to give you a taste of what you could encounter in the nal.
Solving these questions does NOT give you a complete feedback for your exam preparation, some a
IEOR 221 - Spring 2013
Homework 7
Due 04/04/2013
1. Assume that CAPM holds, i.e. ri = r0 + i (m r0 ), where i =
im
2.
m
Your goal is to create a portfolio of stocks X, Y, and the risk-free asset. The beta of
the portfolio is P = 0.70. X has a beta of 1.5
IEOR 221 - Spring 2013
Homework 8
Due 04/11/2013
1. Suppose that a forward contract on an asset is written at time zero and there are T
periods until delivery. Suppose that the carrying charge in period k is qS (k ), where
S (k ) is the spot price of the
IEOR 221: Introduction to Financial Engineering
Sample Final
Name:
(please print)
SID:
Any communication with other students during the exam (including showing, viewing or sharing any writing) is strictly prohibited. Any violation
will result in a score
IEOR 162
Homework 3
Linear Programs & Network Flows - Page 1 of 6 Out: September 7, 2016
Due: September 16, 2016
1. The shaded region of the graph below represents the feasible region of a maximization linear
programming problem.
Use the graph to answer t
Department of Industrial Engineering & Operations Research
IEOR 162 Linear Programming and Network Flows (Fall 2016)
1
1.1
Linear programming modeling examples
Investment problem
You own $1 on Monday and want to invest it to maximize the amount on Friday.
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2016)
Example of an LP with Multiple Optimal Solutions
Maximize
60x1 + 35x2 + 20x3
subject to
8x1 + 6x2
x3
48
4x1 + 2x2 + 1.5x3
20
2x1 + 1.5x2
IEOR 162
Homework 5
Linear Programs & Network Flows - Page 1 of 6Out: September 22, 2016
Due: September 30, 2016
1. (10 points) Recall the following problem from Homework 2: Consider a window company with
only three employees which makes two different kin