# 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
 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 Copyright