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.
Dual variables can be computed using the following formul

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. - 6:00 a.m.
2
6:00 a.m. - 10:00 a.m.
6
10:00 a.m. - 2:00 p.m

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 x1 = Units of Product 1 produced
x2 = Units of Product

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 6.8 Problem 8
The dual objective function is w = .5y1 + .

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 the simplex tableau is:
Row
0
1
2
X2 enters the basis in

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 x1 larger and x2 smaller so we move
down and to the rig

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 which may be formulated as the
following balanced trans

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 variables (Non basic variables) to
0, the remaining 3 by 3 sys

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 + 7x4
st 3x1 + 5x2 + 2x3 + 4x46
xi = 0 or 1
We obtain 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_D o o t 1
All parts ofthe question are inde

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 following table provides
the basic data of the situati

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 the quantities
of the available types of feed (corn, t

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 are in charge of an area where there are | I | number of

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 contributions of a variable xj to the objective function
and t

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 with only two variables
can be solved graphically.
The

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 problem is easy if
the objective function is convex, an

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 an
algorithm which can correctly identify one of
the thr

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 those who provide
funding. The balance sheet presents a s

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. The manager has to help identify
promising projects a

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,
Michelle is a truck short and intends hiring one from a lo