The Simplex Method

1. Basic feasible solutions and pivoting operation,
2. Artificial variable,
3. Degeneracy and cycling,
4. Bland's rule,
5. Klee-Minty twisted cube model and efficiency.

The Duality theorem and dual simplex method

1. The weak duality theorem,
2. The strong duality theorem,
3. Negative transpose property and duality problem,
4. Farkas Lemma and duality theorem,
5. Sensitivity and parametric analysis.

Network flow

1. The Transportation Problem,
2. The Assignment Problem,
3. The Shortest-Path Problem,
4. The Maximum-Flow Problem.

Game theory