IE 202 • Midterm • Operations Research I: Linear Models

What is Linear Programming?

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

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

Example 6 (Minimization)

Example 7 (Minimization)

Example 8 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Direction of Unboundedness

Degeneracy

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

Matrices of LP

Example 1

Forming a Table with Given BV

Example 2

Simplex Method in Matrix Form

Example 3

Example 4

Revised Simplex

Example 5

Example 6

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

Combining with Primal Simplex

Example 3

Example 4

Example 5

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

Linear Programming 1

Linear Programming 2

Linear Programming 3

Linear Programming 4

Linear Programming 5

Linear Programming 6

Linear Programming 7

Linear Programming 8

Graphical Solution 1

Graphical Solution 2

Graphical Solution 3

Graphical Solution 4

Graphical Solution 5

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Simplex Method 5

Simplex Method 6

Big M Method 1

Big M Method 2

Two Phase Method 1

Two Phase Method 2

Duality 1

Duality 2

Duality 3

Duality 4

Matrix Form 1

Matrix Form 2

Revised Simplex

Dual Simplex 1

Dual Simplex 2

Sensitivity Analysis 1

Sensitivity Analysis 2