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Lectures 18-19 Linear Programming

Lectures 18-19 Linear Programming. Preparation Linear Algebra. Linearly Independent. Maximal Independent Subset. Rank of Matrix. Linear Programming. LP examples.

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Lectures 18-19 Linear Programming

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  1. Lectures 18-19Linear Programming

  2. PreparationLinear Algebra

  3. Linearly Independent

  4. Maximal Independent Subset

  5. Rank of Matrix

  6. Linear Programming

  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.

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

  9. Slack Form

  10. What’s a vertex?

  11. Fundamental Theorem

  12. Proof.

  13. Proof (cont’s).

  14. Characterization of Vertex

  15. Proof

  16. Basic Feasible Solution

  17. Optimality Condition

  18. Degeneracy Condition

  19. Sufficiency

  20. Necessary

  21. (pivoting)

  22. Simplex Method

  23. Simplex Table

  24. Puzzle 1

  25. Puzzle 2

  26. lexicographical ordering

  27. Method

  28. Method(cont’)

  29. Method (cont’)

  30. Theorem

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