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

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Presentation transcript:

Linear Programming Chap 2. The Geometry of LP

Linear Programming

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

Linear Programming P A B C D E

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

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

Linear Programming

8

9

Polyhedra in standard form

Linear Programming

Linear Programming

Linear Programming Degeneracy

Linear Programming  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

Linear Programming A B

Linear Programming

Linear Programming Existence of extreme points

Linear Programming

Linear Programming Optimality of extreme points

Linear Programming

Linear Programming