An Economic Interpretation of Linear Programming

This text covers the basic theory and computation for mathematical modeling in linear programming. It provides a strong background on how to set up mathematical proofs and high-level computation methods, and includes substantial background material and direction. Paris presents an intuitive and novel discussion of what it means to solve a system of equations that is a crucial stepping stone for solving any linear program. The discussion of the simplex method for solving linear programs gives an economic interpretation to every step of the simplex algorithm. The text combines in a unique and novel way the microeconomics of production with the structure of linear programming to give students and scholars of economics a clear notion of what it means, formulating a model of economic equilibrium and the computation of opportunity cost in the presence of many outputs and inputs.

Auteur

Quirino Paris spent his entire academic career at the University of California, USA, earning a PhD from Berkeley in 1966 and serving as Professor of Agricultural Economics at UC Davis from 1969. In 2011 he published a companion book titled Economic Foundations of Symmetric Programming. He is a Fellow of the American Applied Economic Association and of the European Association of Agricultural Economists.

Contenu

1. Introduction to Linear Programming
2. Primal and Dual LP Problems
3. Setting Up LP Problems
4. The Transportation and Transshipment Problems
5. Spaces, Cones, Bases and Extreme Points
6. Solving Systems of Equations
7. Primal Simplex Algorithm: The Price-Taking Firm
8. The Dual Simplex Algorithm
9. Linear Programming and the Lagrangean Function
10. The Artificial Variable Algorithm
11. The Artificial Constraint Algorithm
12. The Diet Problem Revisited
13. Parametric Programming: Input Demand Functions
14. Parametric Programming: Output Supply Functions
15. Dealing with Multiple Optimal Solutions
16. Solid Waste Management
17. The Choice of Techniques in a Farm Production Model
18. Cattle Ranch Management
19. The Measurement of Technical and Economic Efficiency
20. Decentralized Economic Planning
21. Theorems of Linear Programming