# Linear Programming and Extensions

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
 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 85 XXIV 89 XXV 94 XXVI 100 XXVII 111 XXVIII 120 XXIX 123 XXX 128 XXXI 134 XXXII 140 XXXIII 144 XXXIV 147 XXXV 156 XXXVI 160 XXXVII 166 XXXVIII 173 XXXIX 177 XL 183 XLI 189 XLII 195 XLIII 202 XLIV 210 XLV 211 XLVI 217 XLVII 221 XLVIII 226 XLIX 228 L 231 LI 237 LII 240 LIII 241 LIV 243 LV 245 LVI 247 LVII 252 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 404 XCI 405 XCII 411 XCIII 413 XCIV 420 XCV 424 XCVI 431 XCVII 433 XCVIII 440 XCIX 446 C 448 CI 455 CII 462 CIII 466 CIV 469 CV 471 CVI 479 CVII 482 CVIII 490 CIX 497 CX 499 CXI 503 CXII 507 CXIII 511 CXIV 514 CXV 521 CXVI 535 CXVII 551 CXVIII 557 CXIX 566 CXX 568 CXXI 580 CXXII 591 CXXIII 616 Copyright

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