1. OR-1 20151 Chapter 2. Simplex method (2,0) (2,2/3) (1,2)(0,2)

2. OR-1 20152

3. 3  Geometry in 2-D 0

4. OR-1 20154 0

5. 5 (4,3) x2x2 x1x1 (2,2/3)

6. OR-1 20156

7. 7 Solving LP graphically  (2,0) (2,2/3) (1,2)(0,2) x2x2 x1x1

8. OR-1 20158 Properties of optimal solutions

9. OR-1 20159 Multiple optimal solutions (2,0) (2,2/3) (1,2)(0,2) x2x2 x1x1

10. OR-1 201510 Obtaining extreme point algebraically (2,0) (2,2/3) (1,2)(0,2) x2x2 x1x1

11. OR-1 201511

12. OR-1 201512

13. Idea of algorithm? OR-1 201513

14. OR-1 201514 Remark: There exists a polyhedron which is not full-dimensional. (extreme point is defined same as before.) x2x2 x1x1 x3x3 1 1 1 This polyhedron is 2-dimensional.

15. OR-1 201515 Algebraic Derivation of Extreme Points for LP

16. OR-1 201516

17. OR-1 201517 x2x2 x1x1 x3x3 1 1 1

18. OR-1 2015 18 =

19. OR-1 201519

20.  Simplex method searches only basic feasible solutions, which is tantamount to searching the extreme points of the corresponding polyhedron until it finds an optimal solution. OR-1 201520