1. Soham Uday Mehta

2. Linear Programming in 3 variables

3. Goals  Visualize the convex feasible region specified by constraints (in 3D)

4. Goals  Visualize the convex feasible region specified by constraints (in 3D)  Visualize Simplex Algorithm to solve the LP (simple version)

5. Visualization  Each constraint becomes a polygon bounding the convex feasible region

6. Visualization

8.  Find the ‘side’ of plane each vertex of polygon is on  If an edge of poly cuts plane, add new vertex and remove the ‘wrong’ side vertex

9. Visualization  Each constraint may also create a new polygon

10. Visualization  Each constraint may also create a new polygon

11. Visualization  Each constraint may also create a new polygon  Store ‘new’ vertices created by clipping existing polygons

12. Visualization  Each constraint may also create a new polygon  Store ‘new’ vertices created by clipping existing polygons  Remove duplicates

13. Visualization  Each constraint may also create a new polygon  Store ‘new’ vertices created by clipping existing polygons  Remove duplicates, re-order vertices, and create new poly

14. Simplex Algorithm 1. Start with a random vertex

15. Simplex Algorithm 1. Start with a random vertex 2. Find extreme directions at current vertex 3. Pick maximum improvement direction 4. If no improvement in any direction, stop

16. Simplex Algorithm 1. Start with a random vertex 2. Find extreme directions at current vertex 3. Pick maximum improvement direction 4. If no improvement in any direction, stop 5. Find max. feasible step and move to next vertex 6. Go back to 2

17. Choosing the start vertex

19. Finding directions at any vertex

21. Finding the next vertex

24. Conclusion  Will be available for downloaddownload

25. Conclusion  Will be available for downloaddownload  Thanks for your attention  Comments / Questions?