PS Handout #1 - INE2008 Operations Research I, Spring 2013
1
1. Farmer Jones
Farmer Jones must determine how many acres of corn and wheat to plant this year.
An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week.
An acre of
BAHEEH R UNIVERSITY
DEPARTMENT OF INDUSTRIAL ENGINEERING
INE2008 OPERATIONS RESEARCH I
Lecture Notes 4
Assist. Prof. Bar Seluk
Spring 2013
7. DUALITY
Definition: The dual problem is an LP defined directly and
systematically from the primal (or original) L
BAHEEH R UNIVERSITY
DEPARTMENT OF INDUSTRIAL ENGINEERING
INE2008 OPERATIONS RESEARCH I
Lecture Notes 5
Assist. Prof. Bar Seluk
Spring 2013
9. TRANSPORTATION MODEL
The problem is to determine the feasible shipping pattern of a
Objective is to determine the
Question Set #3 - INE2008 Operations Research I, Spring 2013
1
1. Consider the following LP.
max
s.t.
z = 5x1 + x2 + 2x3
x1 + x2 + x3 6
6x1 + x3 8
x2 + x3 2
x1 , x2 , x3 0
Let x4 , x5 , and x6 are the slack variables associated with the constraints (1), (
Question Set #1 - INE2008 Operations Research, Spring 2013
1
1. There are three ingredients that need to be included in an animal feed mix. The nal product
must satisfy several nutrient requirements. The possible ingredients, their nutrient contents (as
a
Question Set #2 - INE2008 Operations Research, Spring 2013
1
1. Consider the following LP:
max
z = x1 +3x2
x1 + x2 2
s.t.
x1 + 2x2 4
x1
unrestricted
x2 0
a) Determine all the basic solutions of the problem,
b) Use direct substitution in the objective func
Question Set #4 - INE2008 Operations Research, Spring 2013, by Assist.Prof. Bar Seluk
s
c
1
1. Take the dual of the following LPs:
(a)
Maximize
z = 3x1 + 2x2 + x3
subject to
2x1 + x2 3x3 12
x1 + 2x2 = 10
3x2 + 2x3 6
x1 , x2 0
(b)
Minimize z = x1 2x3
subje
BAHEEH R UNIVERSITY
DEPARTMENT OF INDUSTRIAL ENGINEERING
INE2008 OPERATIONS RESEARCH I
Lecture Notes 2
Assist. Prof. Bar Seluk
Spring 2013
3. GRAPHICAL SOLUTION PROCEDURES
3.1. Definitions
m ax f ( x )
P roblem P
s .t . x B
a)
w here
f ( x ) : any fn o
PS Handout #6 - INE2008 Operations Research I
Spring-2013
1) Consider the given LP below and answer the questions.
min z = 5x1 + x2
s.t. 2x1 + x2 6
x1 + x2 4
x1 + 6 x2 6
x1 , x2 0
a) Find the optimal solution of the LP via graphical method.
b) Consider th
PS Handout #7 - INE2008 Operations Research I
Spring- 2013
1) Powerco has three electric plants that supply the needs of four cities. Each power plant can
supply the following numbers of kilowatt- hours of electricity: plant-1 35 million, plant-2 50 milli
PS #5 - INE2008 Operations Research I, Spring 2013
1
1) Dorian Auto manufactures cars and trucks. To reach their targeted groups, Dorian Auto has
embarked on an TV advertising campaign and decided to purchase 1-minute commercial spots on two
types of prog
BAHEEH R UNIVERSITY
DEPARTMENT OF INDUTRIAL ENGINEERING
INE2008 OPERATIONS RESEARCH I
Lecture Notes 1
Assist. Prof. Bar Seluk
Spring 2013
1. INTRODUCTION TO OPERATIONS RESEARCH
Operations Research (OR) is simply a scientific approach that
seeks to best de
PS Handout #3 - INE2008 Operations Research I
1) Use simplex algorithm to solve the following LP:
max z = 2x1 + 3x2
s.t. x1 + 2x2 6
2x1 + x2 8
x1 , x2 0
2) Use simplex algorithm to nd the optimal solution to the the following LP:
min z = 4x1 x2
s.t. 2x1 +
PS Handout #2 - INE2008 Operations Research I, Spring 2013
1
1. Graphically solve the following LP:
max
z = 2x1 x2
s.t.
x1 x2 1
2x1 x2 6
x1 , x2 0
2. Consider the following problem, where the value of c1 has not yet been decided.
Maximize z = c1 x1 +x2
x1
BAHEEH R UNIVERSITY
DEPARTMENT OF INDUSTRIAL ENGINEERING
INE2008 OPERATIONS RESEARCH I
Lecture Notes 3
Assist. Prof. Bar Seluk
Spring 2013
5. MATRIX REPRESENTATION OF THE SIMPLEX ALGORITHM
An LPs optimal tableau can be expressed in terms of the LPs
parame