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Nydus Open Learning

Mathematics

Mathematics · Advanced · Level 4

Linear programming

Modelling linear programs, the graphical method, the simplex method, duality and sensitivity, integer programming with branch and bound, and network flows.

Ages 18+ 24 lessons about 9 hours in all

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The lessons

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  1. 1 What a linear program decides
  2. 2 The constraint matrix
  3. 3 Standard form
  4. 4 Models that stretch the language
  5. 5 The feasible region
  6. 6 Finding the vertices
  7. 7 Level lines and the best corner
  8. 8 When there is no single answer
  9. 9 Bases and basic feasible solutions
  10. 10 The tableau and the entering variable
  11. 11 The ratio test and one pivot
  12. 12 Termination, degeneracy and the first corner
  13. 13 Forming the dual
  14. 14 Weak and strong duality
  15. 15 Complementary slackness and shadow prices
  16. 16 Sensitivity ranges
  17. 17 Integrality and the relaxation
  18. 18 Modelling with binaries
  19. 19 Branch and bound
  20. 20 Cuts and integral relaxations
  21. 21 Networks as linear programs
  22. 22 Shortest paths
  23. 23 Maximum flow
  24. 24 Cuts, and why flow equals cut