1. Linear Programming 2015 1 Chap 2. The Geometry of LP

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3. 3 Extreme points, vertices, and b.f.s’s

4. Linear Programming 2015 4 P A B C D E

5. 5  Fig. 2.7: A, B, C, D, E, F are all basic solutions. C, D, E, F are basic feasible solutions. P A B C D E F

6. Linear Programming 2015 6  Comparison of definitions in the notes and the text NotesText Extreme point Geometric definition Vertex0-dimensional face Basic solution, b.f.s.

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10. 10 2.3 Polyhedra in standard form

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13. Linear Programming 2015 13 2.4 Degeneracy

14. Linear Programming 2015 14  Fig 2.9: A and C are degenerate basic feasible solutions. B and E are nondegenerate. D is a degenerate basic solution. A B C D E P

15. Linear Programming 2015 15 A B

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17. Linear Programming 2015 17 2.5 Existence of extreme points

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19. Linear Programming 2015 19 2.6 Optimality of extreme points

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