IE 232 • Midterm II + Final • Mathematical Modeling and Optimization

What is duality anyway?

Example 1

Example 2

Example 3

Meaning of Dual Varibles and Complementary Slackness

Example 4

Example 5

Idea Behind Dual Simplex

Comparing Primal/Dual Simplex

Example 1

Example 2

Matrices of LP

Example 1

Forming a Table with Given BV

Example 2

Simplex Method in Matrix Form

Example 3

Example 4

Constraint Slopes

Objective Function Slope

Range of Objective Function Coefficients

Shadow Price

Example

General Procedure

Changing Coefficients of a Non-Basic Variable

Example 1

Example 2

Introducing a New Variable

Example 3

Example 4

Changing Right-Hand-Side of a Constraint

Example 5

Example 6

Introducing a New Constraint

Example 7

Example 8

Changing Coefficients of a Basic Variable

Example 9

Example 10

Definition / LP Solution

Assumptions of the Problem

Least Cost Method

Example 1

Example 2

Northwest Corner Method

Example 3

Example 4

Vogel's Method

Example 5

Transportation Simplex Method

Example 6

Example 7

Transshipment Problem Definition/LP Solution

Example 8

Definition / LP Solution

Assumptions of the Problem

Hungarian Method

Hungarian Method: Trouble in Paradise

Example 1

Example 2

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Representation of LP with Linear Algebra 1

Representation of LP with Linear Algebra 2

Dual Simplex 1

Dual Simplex 2

Dual Simplex 3

Graphical Sensitivity Analysis 1

Graphical Sensitivity Analysis 2

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Transportation Problem 1

Transportation Problem 2

Transportation Problem 3

Transportation Problem 4

Transshipment Problem 1

Assignment Problem 1

Assignment Problem 2

Assignment Problem 3

Assignment Problem 4

Assignment Problem 5