运筹学1至5章习题参考答案

maxZ?x1?2x2?x1?x2?2?(5) ?x1?3??x2?6??x1,x2?0【解】无界解。

minZ?2x1?5x2 (6)

?x1?2x2?6??x1?x2?2?x,x?0?12

【解】无可行解。

1.8 将下列线性规划化为标准形式 maxZ?x1?4x2?x3?2x1?x2?3x3?20 (1)?

?5x1?7x2?4x3?3??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?4x2?x3?x3'''?2x1?x2?3x3?3x3?x4?20?'''?5x1?7x2?4x3?4x3?x5?3 ?'''??10x1?3x2?6x3?6x3?x6?5'''?x,x,x,x?1233,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

maxZ???9x1?3x2?5x3?6x1?7x2?4x3?x4?20??6x?7x?4x?x?201235? ?x?x?5?16??x?8x?82?1??x1,x2,x3,x4,x5,x6?0maxZ?2x1?3x2?1?x1?5 (3)???x1?x2??1?x?0,x?02?1【解】方法1：

maxZ?2x1?3x2?x1?x3?1?x?x?5 ?14??x1?x2?1??x1,x2,x3,x4?0??x1?1,有x1＝x1??1,x1??5?1?4 方法2：令x1??1)?3x2maxZ?2(x1??4?x1???1)?x2??1??(x1?x,x?0?12则标准型为

??3x2maxZ?2?2x1??x3?4?x1???x2?0??x1?x?,x,x?0?123

maxZ?min(3x1?4x2,x1?x2?x3)?x1?2x2?x3?30?(4) ?4x1?x2?2x3?15

??9x1?x2?6x3??5?x1无约束,x2、x3?0?【解】令y?3x1?4x2,y?x1?x2?x3,x1?x1??x1??，线性规划模型变为