Lectures Linear Programming

Preparation Linear Algebra

Linearly Independent

Maximal Independent Subset

Rank of Matrix

Linear Programming

LP examples A post office requires different numbers of full- time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate an LP that the post office can use to minimize the number of full-time employees that must be hired.

Feasible domain Optimal occurs at a vertex!!!

Slack Form

What’s a vertex?

Fundamental Theorem

Proof.

Proof (cont’s).

Characterization of Vertex

Proof

Basic Feasible Solution

Optimality Condition

Degeneracy Condition

Sufficiency

Necessary

(pivoting)

Simplex Method

Simplex Table

Puzzle 1

Puzzle 2

lexicographical ordering

Method

Method(cont’)

Theorem