Linear Programming in Industry

I. Introduction.- A. Planning Company Operations: The General Problem.- B. Linear Planning Models.- C. A Simple Example.- II. Elements of the Mathematical Theory of Linear Programming.- A. The Fundamental Theorem.- B. The Simplex Method and the Simplex Criterion.- III. A Practical Example.- IV. Linear Models of Production and Economic Optimization.- A. The Linear Production Model.- B. Profit Maximization and Cost Minimization.- C. The Basic Assumptions of Linear Programming.- V. Industrial Applications.- A. Blending Problems.- B. Optimal Utilization of Machine Capacities.- C. Inventory Problems.- D. Transportation Problems.- VI. Computational Procedures for Solving Linear Programming Problems.- A. The Simplex Method.- B. The Simplex Tableau.- C. Alternate Optima and Second-Best Solutions.- D. Computational Short Cuts.- E. The Case of Degeneracy.- F. Procedure for Solving Transportation Problems.- VII. Duality in Linear Programming.- A. The Duality Theorem.- B. Economic Interpretation of the Dual.- VIII. The Effects of Coefficient Variations on the Solution.- A. Parametric Programming.- B. A Concrete Example.- IX. The Applicability of Linear Programming in Industry.- A. Linear Programming and Investment Decisions.- B. The Scheduling Problem.- C. Linear Programming versus "Common-Sense" Methods.- A. Proof of the Fundamental Theorem.- B. The Simplex Criterion.- C. The Simplex Algorithm.- D. Proof of the Duality Theorem.- Numerical Exercises.