END 331E • Midterm I • Operations Research I

What is Linear Programming?

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Solving LP with 2 variables

Example 1

Example 2

Example 3

Alternative Optimal Solutions

Example 4

Standard Form of LP

Example 1

Basic Solutions - Basic Feasible Solutions

Example 2

What is Simplex Method?

Example 3

Example 4

Example 5 (Minimization)

Example 6 (Minimization)

Example 7 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Degeneracy

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

Constraint Slopes

Objective Function Slope

Range of Objective Function Coefficients

Shadow Price

Example

What is duality anyway?

Example 1

Example 2

Example 3

Meaning of Dual Varibles and Complementary Slackness

Example 4

Example 5

Model Formulation 1

Model Formulation 2

Model Formulation 3

Model Formulation 4

Model Formulation 5

Model Formulation 6

Graphical Solution Procedure 1

Graphical Solution Procedure 2

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Big M Method 1

Big M Method 2

Big M Method 3

Two Phase Method 1

Two Phase Method 2

Two Phase Method 3

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3