In class exercise #1
Michelles Movers (MM) rents out trucks with a crew of two on a daily basis, usually to
homeowners who are moving or to companies with delivery problems. On one particular day,
Mic
MS 301 SPRING 2014 RECITATION 4 QUESTIONS
These questions are from the textbook Operations Research: Applications and Algorithms by Wayne L.
Winston 4th Ed.
1) Page 154 (Section 4.7) Question 2
Then t
MS 301 SPRING 2014 RECITATION 6 SOLUTIONS
These questions are from Operations Research: Applications and Algorithms by Wayne L. Winston 4th Ed.
1) Page 313 Section 6.7 Problem 3
5) Page 322 Section 6.
MS 301 SPRING 2014 RECITATION 9 SOLUTIONS
These questions are from Operations Research: Applications and Algorithms by Wayne L. Winston 4th Ed.
1. Section 9.2 Question 1
2. Section 9.2 Question 3
Let
MS 301 SPRING 2014 RECITATION 2 SOLUTIONS
1. The below table summarizes Crimevilles requirements for on-duty police officers by the time of day.
Time of Day
Number of Officers Required
2:00 a.m. - 6:0
How to compute dual variables from primal simplex tableau
Let;
cB: objective coefficients of the basic variables
B: matrix formed by the columns of A that belong to (are under) the basic variables.
Du
IE 301
Deterministic Models in
Operations Research
Six types of changes in an LPs parameters change the optimal
solution.
Changing the objective function coefficient of a nonbasic variable.
Changing
IE 301
Week 5
Sensitivity Analysis and Duality
Since all the parameters of an LP model are
estimates, it is essential to check the
robustness of the optimal solution/value with
respect to changes in
IE 301
Week 2
Financial Planning
Suppose you have the following investment
alternatives for the coming 3 years. The cash
flows are given per unit TL.
All cash flows are assumed to be at the end of
t
IE 301 Deterministic Models in
Operations Research
)
Week 1
Origins
World War II
Allocate scarce resources to military
operations and to the activities within each
operation
Organize logistics
Rap
8) Suppose the final tableau of a maximization problem is given as below where x4 and x5
are the slack variables.
Z
1
0
0
x1
0
0
1
x2
4
-1
2
x3
0
1
0
x4
2
1/2
1/2
x5
4
1/2
-1/2
RHS
20
4
2
All parts of
IE 301
Week 3
The Gauss-Jordan Method
Using the Gauss-Jordan method, we can show that any system of
linear equations must satisfy one of the following three cases:
Case 1 The system has no solution.
C
MS 301 SPRING 2014 RECITATION 1
SOLUTIONS
Printed questions are from the textbook Operations
Research: Applications and Algorithms by Wayne L.
Winston 4th Ed.
Section 3.2
Solution
4a. We want to make
MS 301 SPRING 2014 RECITATION 8 SOLUTIONS
These questions are from Operations Research: Applications and Algorithms by Wayne L. Winston 4th Ed.
1) Page 418 Section 8.2 Problem 4
transshipment problem
Lecture 1
Goals and Governance of the
Firm &
Financial Markets and
Institutions
The Investment (Capital Budgeting)
Decision
The first task of the financial manager is making good
investment decisions
Lecture 2
Accounting and Finance
The Balance Sheet
Firms need to raise cash to pay for the many assets used
in their business. In the process of raising that cash,
they also acquire liabilities to th
3/9/2016
IE 301
Deterministic Models in
Operations Research
Lecture 5
Different Forms of an LP
Problem Manipulation
Kerem Blbl
Different representations of an LP
From now on, our goal is to develop a
3/18/2016
IE 301
Deterministic Models in
Operations Research
Lecture 7
An Introduction to Convex Analysis
Kerem Blbl
Relation to optimization
In our previous lectures, we argued that a
minimization p
10/26/2016
IE 301
Deterministic Models in
Operations Research
Lecture 4
Linear Programming in Two Dimensions
Graphical Solution & Insights
Kerem Blbl
Graphical Solution to a 2-Variable LP
X2
4
Any LP
2/23/2016
IE 301
Deterministic Models in
Operations Research
Lecture 3
Assumptions in Linear Programming
Formulation Examples
Kerem Blbl
Assumptions in linear programming
Proportionality
The contrib
IE 301
Assignment 2
Fall 2016
Due at 5:30pm on October 24, 2016
Question 1
As an ocer of the local UNICEF oce, your task is to manage the administration of the next vaccine
shots. In particular, you a
IE301 Recitation 1
Questions & Solutions
1) Fred Jonson manages a family-owned farm. To supplement several food products grown
on the farm, Fred also raises pigs for market. He now wishes to determine
IE301 Recitation 2
Questions & Solutions
1) A city will undertake five urban renewal housing projects over the next five years. Each
project has a different starting year and a different duration. The
Suppose the final tableau of a maximization problem is given as below where M and x5.
are the slack variablesr
Z x. x 1 x3 x5 RHS
1 u ,E I :1 Pa 20
1 1 H' 4
0 1 2 0 2
0 o o cfw_
MS 301 SPRING 2014 RECITATION 10 SOLUTIONS
1. Section 9.3 page 522 Question 1
Letting xi = 1 if item i is chosen and xi = 0 otherwise
yields the following knapsack problem:
max z = 5x1 + 8x2 + 3x3 + 7
MS 301 SPRING 2014 RECITATION 3 SOLUTIONS
1) Consider a linear programming problem with 3 constraints and 5
variables in standard form. Find A and b such that
a. When you set a certain pair of variabl
1) Suppose the final tableau of a maximization problem is given as below where s1 and s2
are the slack variables associated with the first and second constraints respectively.
Z
x1
x2
x3
s1
s2
1
6
0
0