IE 202 • Quiz 3 + 4 • Introduction to Modeling and Optimization

Magic of Linear Algebra

Matrices of LP

Forming a Table

Example 1

One Formula to Rule Them All

Example 2

Dual of an LP

Examples 1-2

Example 3

Weak Duality Theorem

Strong Duality Theorem

Shadow Price

Complementary Slackness

Example 4

Example 5

Dual Solution

Primal/Dual Feasibility and Optimality

Example 6

Matrix Form 1

Matrix Form 2

Matrix Form 3

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Duality 7

Duality (Fall 23 - Quiz III)

Duality (Spring 25 - Quiz III)

Duality (Fall 24 - Quiz III)

Duality (Spring 25 - Quiz III)

Duality (Spring 25 - Quiz III)

Duality - Matrix Form (Fall 23 - Quiz III)

Duality - Matrix Form (Fall 24 - Quiz III)

Duality - Matrix Form (Spring 25 - Quiz III)

Duality - Matrix Form (Fall 23 - Quiz III)

Duality - Matrix Form (Fall 23 - Quiz III)

Idea Behind Dual Simplex

Comparing Primal/Dual Simplex

Example 1

Example 2

Combining with Primal Simplex

Example 3

Example 4

Example 5

General Procedure

Optimal Basis v Optimal Solution

Changing Objective Function Coefficient of a NBV

Example

Changing Objective Function Coefficient of a BV

Example

Changing RHS of a Constraint

Example

Changing Column of a NBV

Example

Adding a New Variable

Example

Adding a New Constraint

Example

Dual Simplex 1

Dual Simplex 2

Dual Simplex 3

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Sensitivity Analysis 4

Sensitivity Analysis 5

Sensitivity Analysis 6

Sensitivity Analysis (Fall 24 - Quiz IV)

Sensitivity Analysis (Spring 25 - Quiz IV)

Sensitivity Analysis (Fall 23 - Final)

Sensitivity Analysis (Fall 21 - Final)

Sensitivity Analysis (Spring 20 - Quiz IV)