Linear Programming

One: Convex Sets.- 1. Convex hulls, polytopes and vertices.- 2. Basic solutions of equations.- 3. Theorem of the separating hyperplane.- 4. Alternative solutions of linear inequalities 10 Exercises.- Two: The Theory of Linear Programming.- 1. Examples and classes of linear programmes.- 2. Fundamental duality theorem.- 3. Equilibrium theorems.- 4. Basic optimal vectors.- 5. Graphical method of solution.- Exercises.- Three: The Transportation Problem.- 1. Formulation of problem and dual.- 2. Theorems concerning optimal solutions.- 3. Method of solution with modifications for degeneracy.- 4. Other problems of transportation type.- Exercises.- Four: The Simplex Method.- 1. Preliminary discussion and rules.- 2. Theory of the simplex method.- 3. Further techniques and extensions.- Exercises.- Five: Game Theory.- 1. Two-person zero-sum games.- 2. Solution of games: saddle points.- 3. Solution of games: mixed strategies.- 4. Dominated and essential strategies.- 5. Minimax theorem.- 6. Solution of matrix games by simplex method.- Exercises.- Suggestions for Further Reading.- Solutions to Exercises.