1. The Linear Programming Concept -- 2. Origins and Influences -- 3. Formulating a Linear Programming Model -- 4. Linear Equation and Inequality Systems -- 5. The Simplex Method -- 6. Proof of the Simplex Algorithm and the Duality Theorem -- 7.
The Geometry of Linear Programs -- 8. Pivoting, Vector Spaces, Matrices, and Inverses -- 9. The Simplex Method Using Multipliers -- 10. Finiteness of the Simplex Method Under Perturbation -- 11. Variants of the Simplex Algorithm -- 12. The Price Concept in Linear Programming -- 13. Games and Linear Programs -- 14. The Classical Transportation Problem -- 15. Optimal Assignment and Other Distribution Problems -- 16. The Transshipment Problem -- 17. Networks and the Transshipment Problem -- 18. Variables with Upper Bounds -- 19. Maximal Flows in Networks -- 20. The Primal-Dual Method for Transportation Problems -- 21. The Weighted Distribution Problem -- 22. Programs with Variable Coefficients -- 23. A Decomposition Principle for Linear Programs -- 24. Convex Programming -- 25. Uncertainty -- 26. Discrete Variable Extremum Problems -- 27. Stigler's Nutrition Model: An Example of Formulation and Solution -- 28. The Allocation of Aircraft to Routes Under Uncertain Demand

A basic text in linear programming, the solution of systems of linear equalities. The subjects covered include the concepts, origins and formulations of linear programs, and the simplex method of solution as applied to the price concept, matrix games, and transportation problems. Also included is the background, on convex sets and linear spaces, necessary to forward the discussion on such topics as duality, variants of the simplex method, and the extensions of linear programming to convex programs, to programming under uncertainty, and to certain network, topological, and combinatorial problems that may be couched in the form of linear inequalities with integer-valued variables.