The Dual Problem
PrimalDual Relationships
Duality
March 18, 2015
Duality
Economic Interpretation of Duality
The Dual Problem
Table of contents
Duality
PrimalDual Relationships
Economic Interpretation of Duality
The Dual Problem
PrimalDual Relationships
The Dual Problem
PrimalDual Relationships
Duality
March 25, 2015
Duality
Economic Interpretation of Duality
The Dual Problem
PrimalDual Relationships
Table of contents
The Dual Problem
PrimalDual Relationships
Economic Interpretation of Duality
Duality
Sensitivity Analysis
March 30, 2015
Sensitivity Analysis
March 30, 2015
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Sensitivity Analysis
Changes in Parameters
Sensitivity analysis investigates the change in the optimum solution
resulting from making changes in parameters of the LP model.
Sen
A ProductMix Problem
HiTech Inc., a small manufacturing firm produces two microwave switches, Switch A and Switch
B. The return per unit of Switch A is $20, whereas the return per unit of Switch B is $30.
Because of contractual commitments, HiTech must m
ISMATH3 PROBLEM SET
1. A furniture maker has 6 units of wood and 28 hours of free time, in which he will make
decorative screens. Two models have sold well in the past, so he will restric himself to those two.
He estimates that model I requires 2 units of
ISMATH3
Problem Set 3
I. Determine the type of aberration in the following
LP models, and solve the optimal solution (if
applicable).
(a) Maximize z = x1 + x2
Subject to
x1 + x2 4
x1 x2 5
x1 , x2 0
400x1 + 200x2 + 150x3 + 500x4
3x1 + 2x2
2x1 + 2x2 + 4x3 +
Review on Matrix Operations
March 17, 2015
Order of a Matrix
Order of a Matrix
A matrix having m rows and n columns is said to be of order m n.
Determine the order of each matrix
1
2
0 1
2
7 2
5
0
3 2
2
7 4
1
4
1 3 0
8
Transpose of a Matrix
Transpose of
Graphical Sensitivity
Analysis
Sensitivity Analysis
how sensitive the optimal solution is to changes in data
values
Example:
What effect does increasing the number of workers have on the
optimal solution?
If we change the objective function, will we sti
ISMATH3 Chapter 1
Operations Research the use of advanced analytical techniques to improve decision making.

Needed to make the best use of available resources
The first formal activities of OR were initiated in England during World War II when a team of
DALANGIN, Philip Minh S.
ELECTRA Exercise
Decision variables
X1 = type 1 motor
X2 = type 2 motor
Objective function
Max z = 60x1 + 40x2
Subject to
10X1 +8 X2 8000
X1,x2 0
X1 600
X2 750
Constraints

daily capacity of assembly line 1 is 600
daily capacity
ISMATH3 Chapter 1
Operations Research the use of advanced analytical techniques to improve decision making.

Needed to make the best use of available resources
The first formal activities of OR were initiated in England during World War II when a team of
Exercises (Feb 23, 2015)
Solve the following linear programming models using the appropriate method.
max z=4 x1 +3 x 2
1.
Subject to:
x 1 + x 2 6
2 x 1 + x 2 20
x 1+ x 2 12
x1 , x2 0
2.
min z=5 x 1 +2 x 2
Subject to:
x 1 12
x 1 +2 x2 8
x2 8
2 x 1 +3 x 2 3