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maxZ?x1?4x2?x1?4x2?5?(2) ?x1?3x2?2??x1?2x2?4??x1,x2?0
【解】有多重解。最优解R
(1)
=(0,5/4);R
(2)
=(3,1/2)最优值Z=5
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minZ??3x1?2x2?x1?2x2?11??x?4x?1012(3)???2x1?x2?7?x?3x?12?1??x1,x2?0
【解】最优解R=(4,1);最优值Z=-10,有唯一最优解
minZ?4x1?6x2?x1?2x2?8?(4) ?x1?x2?8?x2?3???x1?0,x2?0
【解】最优解R=(2,3);最优值Z=26,有唯一最优解
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maxZ?x1?2x2?x1?x2?2?(5) ?x1?3??x2?6??x1,x2?0【解】无界解。
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minZ?2x1?5x2?x1?2x2?6 (6)??x1?x2?2?x,x?0?12【解】无可行解。
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1.7 将下列线性规划化为标准形式 minZ?x1?6x2?x3?x1?x2?3x3?15 (1) ?
?5x1?7x2?4x3?32??10x1?3x2?6x3??5??x1?0,x2?0,x3无限制'''【解】(1)令x3?x3?x3,x4,x5,x6为松驰变量 ,则标准形式为
'''maxZ??x1?6x2?x3?x3'''?x1?x2?3x3?3x3?x4?15?'''?5x1?7x2?4x3?4x3?x5?32 ?'''?10x?3x?6x?6x?x6?51233?'''??x1,x2,x3,x3,x4,x5,x6?0minZ?9x1?3x2?5x3?|6x1?7x2?4x3|?20? (2) ?x1?5 ??x1?8x2??8??x1?0,x2?0,x3?0【解】(2)将绝对值化为两个不等式,则标准形式为
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