In real-world problems related to finance, business, and
management, mathematicians and economists frequently encounter
optimization problems. In this classic book, George Dantzig looks
at a wealth of examples and develops linear programming methods for
their solutions. He begins by introducing the basic theory of
linear inequalities and describes the powerful simplex method used
to solve them. Treatments of the price concept, the transportation
problem, and matrix methods are also given, and key mathematical
concepts such as the properties of convex sets and linear vector
spaces are covered.
George Dantzig is properly acclaimed as the "father of linear
programming." Linear programming is a mathematical technique used
to optimize a situation. It can be used to minimize traffic
congestion or to maximize the scheduling of airline flights. He
formulated its basic theoretical model and discovered its
underlying computational algorithm, the "simplex method," in a
pathbreaking memorandum published by the United States Air Force in
early 1948. "Linear Programming and Extensions" provides an
extraordinary account of the subsequent development of his subject,
including research in mathematical theory, computation, economic
analysis, and applications to industrial problems.
Dantzig first achieved success as a statistics graduate student
at the University of California, Berkeley. One day he arrived for a
class after it had begun, and assumed the two problems on the board
were assigned for homework. When he handed in the solutions, he
apologized to his professor, Jerzy Neyman, for their being late but
explained that he had found the problems harder than usual. About
six weeks later, Neyman excitedly told Dantzig, "I've just written
an introduction to one of your papers. Read it so I can send it out
right away for publication." Dantzig had no idea what he was
talking about. He later learned that the "homework" problems had in
fact been two famous unsolved problems in statistics.
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