Linear Programming and Extensions

Front Cover
Princeton University Press, 1998 - Mathematics - 627 pages

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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Contents

II
1
III
6
IV
7
V
10
VI
12
VII
16
VIII
20
IX
28
LXVI
277
LXVII
286
LXVIII
291
LXIX
297
LXX
299
LXXI
300
LXXII
308
LXXIII
314

X
32
XI
34
XII
35
XIII
42
XIV
50
XV
55
XVI
57
XVII
60
XVIII
62
XIX
69
XX
75
XXI
81
XXII
84
XXIII
85
XXIV
89
XXV
94
XXVI
100
XXVII
111
XXVIII
120
XXIX
123
XXX
128
XXXI
134
XXXII
140
XXXIII
144
XXXIV
147
XXXVII
156
XXXVIII
160
XXXIX
166
XL
173
XLI
177
XLII
183
XLIII
189
XLIV
195
XLV
202
XLVI
210
XLVII
211
XLVIII
217
XLIX
221
L
226
LI
228
LII
231
LIII
237
LIV
240
LV
241
LVI
243
LVII
245
LVIII
247
LIX
252
LX
253
LXI
254
LXII
260
LXIII
264
LXIV
265
LXV
275
LXXIV
316
LXXV
322
LXXVI
330
LXXVII
332
LXXVIII
335
LXXIX
342
LXXX
346
LXXXI
351
LXXXII
352
LXXXIII
357
LXXXIV
361
LXXXV
366
LXXXVI
368
LXXXVIII
377
LXXXIX
383
XC
385
XCI
398
XCII
403
XCIII
404
XCIV
405
XCV
411
XCVI
413
XCVII
420
XCVIII
424
XCIX
431
C
433
CI
440
CII
446
CIII
448
CIV
455
CV
462
CVI
466
CVII
469
CVIII
471
CIX
479
CX
482
CXI
490
CXII
497
CXIII
499
CXIV
503
CXV
507
CXVI
511
CXVII
514
CXVIII
521
CXIX
535
CXXI
551
CXXII
557
CXXIII
566
CXXIV
568
CXXV
580
CXXVI
589
CXXVII
614
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About the author (1998)

George B. Dantzig is Professor Emeritus in the Department of Engineering-Economic Systems and Operations Research at Stanford University.

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