Chapter 7 Linear Programming I. Simplex Method Ding-Zhu Du

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

Whats a vertex?

Fundamental Theorem

Proof.

Proof (conts).

Characterization of Vertex

Proof

Basic Feasible Solution

Optimality Condition

Sufficiency

Nondegeneracy Assumption Remark

Necessary

(pivoting)

Simplex Method

Simplex Table

Puzzle 1

Artificial Feasible Basis

Puzzle 2

lexicographical ordering

Method

Method(cont)

Theorem

Puzzle 3

Complexity of LP

Thanks, End