Linear Programming and Extensions

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Princeton University Press, 1998 - Mathematics - 627 pages
1 Review

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
LXIV
277
LXV
286
LXVI
291
LXVII
297
LXVIII
299
LXIX
300
LXX
308
LXXI
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
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XXIV
89
XXV
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XXVI
100
XXVII
111
XXVIII
120
XXIX
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XXX
128
XXXI
134
XXXII
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XXXIII
144
XXXIV
147
XXXV
156
XXXVI
160
XXXVII
166
XXXVIII
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XXXIX
177
XL
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XLI
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XLII
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XLIII
202
XLIV
210
XLV
211
XLVI
217
XLVII
221
XLVIII
226
XLIX
228
L
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LI
237
LII
240
LIII
241
LIV
243
LV
245
LVI
247
LVII
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LVIII
253
LIX
254
LX
260
LXI
264
LXII
265
LXIII
275
LXXII
316
LXXIII
322
LXXIV
330
LXXV
332
LXXVI
335
LXXVII
342
LXXVIII
346
LXXIX
351
LXXX
352
LXXXI
357
LXXXII
361
LXXXIII
366
LXXXIV
368
LXXXV
377
LXXXVI
383
LXXXVII
385
LXXXVIII
398
LXXXIX
403
XC
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XCI
405
XCII
411
XCIII
413
XCIV
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XCV
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XCVI
431
XCVII
433
XCVIII
440
XCIX
446
C
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CI
455
CII
462
CIII
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CIV
469
CV
471
CVI
479
CVII
482
CVIII
490
CIX
497
CX
499
CXI
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CXII
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CXIII
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CXIV
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CXV
521
CXVI
535
CXVII
551
CXVIII
557
CXIX
566
CXX
568
CXXI
580
CXXII
591
CXXIII
616
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