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

7. 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.

12. Feasible domain Optimal occurs at a vertex!!!

13. Slack Form

14. Whats a vertex?

15. Fundamental Theorem

16. Proof.

17. Proof (conts).

18. Characterization of Vertex

19. Proof

20. Basic Feasible Solution

21. Optimality Condition

22. Sufficiency

23. Nondegeneracy Assumption Remark

24. Necessary

26. (pivoting)

27. Simplex Method

28. Simplex Table

35. Puzzle 1

36. Artificial Feasible Basis

37. Puzzle 2

38. lexicographical ordering

39. Method

40. Method(cont)

42. Theorem

43. Puzzle 3

44. Complexity of LP

45. Thanks, End