INDUSTRIAL ENGINEERING DEPARTMENT
INTRODUCTION TO OPERATIONS RESEARCH I
Solutions to LP Models
Problem Set II
1.
A comparison shopper is trying to select the cheapest combination of two foods to
meet
INDUSTRIAL ENGINEERING DEPARTMENT
INTRODUCTION TO OPERATIONS RESEARCH I
Problem Set I
MODEL FORMULATION
1. The Alambre Corporation makes two types of copper wire: Type 1 (rubber-insulated) and Type 2
DUALITY THEORY
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DUALITY THEORY
LP problems always exist in pairs. The original LP problem
is known as the primal model while its complementary
model is known as the dual.
Symmetric (canonical
ABCO Manufacturing
ABCO manufactures 2 products X and Y. ABCO's manager is interested in production and
liquidity planning for the next 2 weeks of operation. The first week has four working days and t
LP
O
I
T
U
SOL
N
SPECIAL CASES
I. NO FEASIBLE SOLUTION
there is no point which will satisfy all
the constraints
Indicators:
The graph produces no feasible region.
The optimal tableau contains R as b
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Introduction to Model Building
Operations Research: Applications & Algorithms
4th edition, by Wayne L. Winston
Definition of Operations Research
Operations Research (management
science) is a
Gokongwei College of Engineering
Department of Industrial Engineering
De La Salle University
Vision Corporation:
Production Planning and Shipping
In partial fulfillment of the requirements for
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INTRODUCTION TO OPERATIONS RESEARCH I
Problem Set
Sensitivity Analysis
1. A manufacturing firm has discontinued production of certain unprofitable product line. This
created considerable excess produc
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study of the effects of the changes in
parameter values on the present basic
optimal solution
Parameters: OFC C
Constraint Coefficients A
RHS b
Present Basic Optimal Solution XB
-refers to th
Increasing the demand for RAYco by 50% can be handled by the current system. Labor time for each of
three plants are not fully utilized which means that the unused capacity for the labor time can be u
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PROBLEM SET
DUALITY
1. For each of the following, formulate the dual.
a.
Min
Z 20 x1 15 x 2
s.t. 2 x1 x 2 5
3x1 2 x 2 3
x1 x 2 3
x1 , x 2 0
b.
Max
Z 15 x1 25 x 2 10 x3
s.t. 6 x 2 3 x3 12
3 x1
LP
O
I
T
U
SOL
N
SPECIAL CASES
I. NO FEASIBLE SOLUTION
there is no point which will satisfy all
the constraints
Indicators:
The graph produces no feasible region.
The optimal tableau contains R as b
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DEPA RTM ENT OF INDUSTRIAL ENGINEERING
OPERATIONS RESEARCH l
Quiz No. 3
luv/rm 'Iinnv'
l
.2 .
llns is a closed notes.
Initiallv draw the network din am for the tr ortation network of the mm anv: Formulate the linear r ammin model for the rolJlem as shown below:
Let:
x3 = Products shippedfrom Plant i to Customer R [
INDUSTRIAL MANAGEMENT ENGINEERING SOCIETY
ERGBIO1REVIEWERforQuiz#1
I.
True or False
1. Treatment using vibration has been advocated for improving joint mobility.
2. Hennings smell prism employs five p