1. Linear Program MAX C B X B + C NB X NB s.t. BX B + A NB X NB = b X B, X NB ≥ 0

2. Important LP Equations

3. Important LP Derivatives

4. Duality

6. Unbounded Solution

7. Infeasible Solution

8. Multiple Optima

9. Degeneracy

10. Complementary Slackness derived from duality

11. Reduced Cost Negative derivative of objective function with respect to a variable At optimality: –Zero for all basic variables –Non-negative for all non-basic variables (max) –Non-positive for all non-basic variables (max)

12. Multi-input, Multi-output

13. Mixing / Blending

14. Spatial Equilibrium (GAMS Ex.)

15. Sequencing

17. Storage

18. Lexicographic preferences

19. Weighted Preferences

20. Well behaved, Separable Function

23. Disequilibrium – Known Life

24. Disequilibrium – Unknown Life

25. Equilibrium ‑ Unknown Life

26. Fixed Costs

27. Fixed Capacity

28. Minimum Habitat Size

30. Warehouse

31. Mutual exclusive products

32. Either-Or-Active constraints

33. Distinct Variable Values

34. Badly behaved non-linear functions

36. Non-linear Programming Specification often straightforward Solving more difficult –scaling (manual vs. computer) –lower bounds to avoid division by zero and other illegal operations –local versus global extremes