hw4Spring2011 - ÅØ ¾ ËÔÖ Ò ¾¼½½ ËÓÑ ØÖ ÓØ...

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Unformatted text preview: ÅØ ¾ ËÔÖ Ò ¾¼½½ ËÓÑ ØÖ ÓØ × ÔÖÓ Ð Ñ× Ö ÕÙ Ö ÔÖÓ Ð Ñ׺ Ù ½º ÅÖ Ò ÅÒÑÞ ÀÓÑ ÛÓÖ × ÛÓÖØ 4 Ø ¾¹Ô × × ÑÔÐ Ü Ñ Ø Ó ¸ Û Û Û ÐÐ ÓÚ Ö Ò Ð ØÙÖ º Ó ÐÐ ÔÓ ÒØ׺ ¾¸ ¾¼½½ Ø Ù Ð ØÓ Ø y1 + 2 y2 + y3 ÓÐÐÓÛ Ò ×Ù Ñ Ò ÑÙÑ ÔÖÓ Ð Ñº Ø ØÓ y1 − 2 y2 + y3 ≥ 2 −y1 + y2 + y3 ≥ 4 2 y1 + y3 ≥ 6 y1 + y2 + y3 ≥ 2 Ò ÐÐ ¾º yi ≥ 0 º ´ ÜÔÖ ×× Ø ÙÐ × Ñ Ü Ñ Þ Ø ÓÒ ÔÖÓ Ð Ñºµ Û Ø ÓÙØ Ù× Ò Ø × ÑÔÐ Ü Ñ Ø Ó Ò (x1 , x2 , x3 , x4 ) = (0, 1/3, 2/3, 0) × ÓÔØ Ñ Ð ÓÖ Ø ÄÈ Å Ü Ñ Þ 3x1 + 2x2 + x3 ×Ù Ø ØÓ ÓÖ É½¸ × ÓÛ ÔÖ Ñ Ð ¿º Ø Ø (y1 , y2 , y3 ) = (2/3, 0, 14/3) ÓÖ Ø × ÓÔØ Ñ Ð ÓÖ Ø Ù Ðº x1 − x2 + x3 ≤ 4 2x1 + x2 + 3x3 ≤ 6 −x1 + 2x3 ≤ 3 x1 + x2 + x3 ≤ 8 Ò ÐÐ xi ≥ 0 ´ µ ËØ Ø Ø ´ µ ËÙÔÔÓ× Ù Ð Ñ Ò Ñ Þ Ø ÓÒ ÔÖÓ Ð Ñº ÝÓÙ Ù ×× Ø ÔÐ Ñ ÒØ ÖÝ ×Ð Ò ×× ØÓ ×ÓÐÚ ÔÖÓ Ð Ñ × Ø (x1 , x2 , x3 ) = (0, 6, 0) غ ÓÖÖ Ø Ù Ð ÔÖÓ Ð Ñ Ò × ÓÔØ Ñ Ð ÓÖ Ø ÔÖÓÚ ½ ÓØ ÝÓÙÖ ÔÖ Ñ Ð ´Ñ ܵ ÔÖÓ Ð Ñº Í× Ù ×× Ò ÝÓÙÖ ×ÓÐÙØ ÓÒ ØÓ Ø Óѹ ÙÐ ...
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This note was uploaded on 02/19/2012 for the course MATH 482 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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