运筹学(第3版) 习题答案 5

即

x4410x454x463?,?,? x454x463x471半成品油供应量约束

x11?x21?2000x12?x22?1000x13?x23?1500x34?x44?1200 x35?x45?1000x36?x46?1000x37?x47?800整理后得到

maxZ?5x11?5x12?5x13?4.2x21?4.2x22?4.2x23?3x34?3x35?3x36?3x37?1.5x44?1.5x45?1.5x46?1.5x47??14x11?21x12?11x13?0???14x21?21x22?11x23?0??4x21?31x22?21x23?0??0.5x35?0.4x36?0.95x37?0?4x?10x?045?44?3x45?4x46?0??x46?3x47?0??x11?x21?2000?x?x?1000?1222?x13?x23?1500??x34?x44?1200?x35?x45?1000??x36?x46?1000?x?x?800?3747??xij?0;i?1,2,3,4;j?1,2,,71.6 图解下列线性规划并指出解的形式：

maxZ?5x1?2x2?2x1?x2?8?(1) ?x1?3??x2?5??x1,x2?0

【解】最优解X＝（3，2）；最优值Z=19

运筹学(第3版) 习题答案 6

maxZ?x1?4x2?x1?4x2?5?(2) ?x1?3x2?2??x1?2x2?4??x1,x2?0

【解】有多重解。最优解X

（1）

＝（0，5/4）；X

（2）

＝（3，1/2）最优值Z=5

运筹学(第3版) 习题答案 7

minZ??3x1?2x2?x1?2x2?11??x?4x?1012(3)???2x1?x2?7?x?3x?12?1??x1,x2?0

【解】最优解X＝（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X＝（2，3）；最优值Z=26，有唯一最优解

运筹学(第3版) 习题答案 8

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