Lectures 18-19 Linear Programming

1. Lectures 18-19Linear Programming

2. PreparationLinear Algebra

3. Linearly Independent

4. Maximal Independent Subset

5. Rank of Matrix

6. Linear Programming

13. 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.

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

23. Slack Form

24. What’s a vertex?

25. Fundamental Theorem

26. Proof.

27. Proof (cont’s).

28. Characterization of Vertex

29. Proof

30. Basic Feasible Solution

31. Optimality Condition

32. Degeneracy Condition

33. Sufficiency

34. Necessary

36. (pivoting)

37. Simplex Method

38. Simplex Table

44. Puzzle 1

45. Puzzle 2

46. lexicographical ordering

47. Method

48. Method(cont’)

49. Method (cont’)

50. Theorem