Linear Programming and Extensions (Princeton Landmarks in Mathematics and Physics, 25)

In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. First published in 1963, this classic work looks at a wealth of examples and develops linear programming methods for solutions. Treatments covered include price concepts, transportation problems, matrix methods, and the properties of convex sets and linear vector spaces. The influential book that established the mathematical discipline of linear programmingIn the worlds of finance, business, and management, mathematicians and economists frequently encounter problems of optimization. In this classic book, George Dantzig shows how the methods of linear programming can provide solutions. Drawing on a wealth of examples, he introduces the basic theory of linear inequalities and describes the powerful simplex method used to solve them. He discusses the price concept, the transportation problem, and matrix methods, and covers key mathematical concepts such as the properties of convex sets and linear vector spaces. Dantzig demonstrates how linear programming can be applied to a host of optimization problems, from minimizing traffic congestion to maximizing the scheduling of airline flights.An invaluable resource for students and practitioners alike, Linear Programming and Extensions is an extraordinary account of the development and uses of this versatile mathematical technique, blending foundational research in mathematical theory with computation, economic analysis, and applications to industrial problems.