第1章训练题
一．基本技能训练
1．用图解法求解下列线性规划问题
minz?4x1?6x2?5x1?10x2?50?x1?3x2?3（1）?x?x?1 （2）?
?12x?x?2?12?x2?4?x,x?0??12??x1,x2?0maxz?x1?3x2maxz?2x1?2x2?x1?x2??1（3）???0.5x1?x2?2?x,x?0?121．用图解法求解下列线性规划问题
maxz?2x1?2x2?x1?x2?0 （4）??3x1?x2??3?x,x?0?12
(1). 唯一最优解X*?(2,4)T,z*?14； (2). 唯一最优解X?(,),z?9； (3). 无界解； (4). 无可行解；
2．用单纯形法求解下列线性规划问题
*3122T*maxz?2x1?x2?x3?3x1?x2?x3?60x1?4?（1）?2x?12 （2） ??x1?x2?2x3?10 ?2??3x?2x?18?x1?x2?x3?202?1???x1,x2,x3?0?x1,x2?0maxz?6x1?2x2?10x3?8x4?5x1?6x2?4x3?4x4?20（3）??3x1?3x2?2x3?8x4?25 （4）
??4x1?2x2?x3?3x4?10?x1,x2,x3,x4?0?maxz?x1?6x2?4x3??x1?2x2?2x3?13?4x?4x?x?20 ?123??x1?2x2?x3?17??x1?1,x2?2,x3?3maxz?3x1?5x2maxz?2x1?3x2?5x3maxz?90x1?160x2?40x3?100x4?2x1?2x2?3x3?12?2x1?8x2?4x3?2x4?480?x?2x?2x?8?5x?4x?8x?5x?800123（5）? （6） ?1234???4x1?6x3?16?7x1?8x2?3x3?5x4?900?4x?3x?1223???x1,x2,x3,x4?0?x,x,x?0?123第 1 页 共 30 页
minz?1000x1?800x2?1?x1minz?2x1?3x2?x3?0.8x?x?1.6?x1?4x2?2x3?812??（7） （8）?
?23x?2x?6?x1?12??x,x,x?0x2?1.4?123???x1,x2?0maxz?10x1?15x2?12x3?5x1?3x2?x3?9（9）???5x1?6x2?15x3?15??2x1?x2?x3?5??x1,x2,x3?0maxz?2x1?x2?2x3?x1?x2?x3?6（11）?x3?2 （12） ??2x1??2x2?x3?0???x1,x2,x3?0maxz?x1?2x2?3x3?x4?15?x1?2x2?3x3 （10） ??20 ?2x1?x2?5x3??x1?2x2?x3?x4?10??x1,x2,x3,x4?0maxz?5x1?3x2?6x3?x1?2x2?x3?18?2x?x?3x?16 ?123??x1?x2?x3?10??x1,x2?0，x3无约束minz?x1?3x2（13）?maxz?5x1?8x2 （14）??x1?2x2?6?x1?x2?5?x,x?0?12?3x1?2x2?6?x1?2x2?1?x,x?0?12
maxz?x1?2x2?x3minz?x1?2x2?3x3?x1?x2?x3?12??2x1?x2?3x3?2（15）? （16）?2x?x?x?6
?123?2x1?3x2?4x3?10??x,x,x?0??x1?3x2?9?123??x1,x2,x3?0minz??2x1?x2?3x3?5x4?x1?2x2?4x3?x4?6（17）??2x1?3x2?x3?x4?12??x1?x3?x4?4??x1,x2,x3,x4?0minz?3x1?2x2??x1?3x2??3??2x?x??612 （18）? ??2x1?x2?8?4x?x?162?1??x1,x2?0maxz?x1?3x2?4x3?3x1?2x3?13（19）??x2?3x3?17??2x1?x2?x3?13??x1,x2,x3?0minz?x1?3x2?x3?x1?x2?x3?3 （20）? ??x1?2x2?2???x1?5x2?x3?4??x1,x2,x3?0第 2 页 共 30 页
minz?8400x1?7500x2?6700x380x3?70? 60x1? 65x2? （21）??3800x1?3500x2?2500x3?2900
?x3?1? x1? x2? ??x1,x2,x3?0maxz?2x1?3x2?4x3?7x4（22）??2x1?3x2?x3?4x4?8?x1?2x2?6x3?7x4??3?x1,x2,x3,x4?0?*
(22). 唯一最优解X?(347117,0,0,)T,z*?； 555minz?5x1?2x2?3x3?6x4（23）??x1?2x2?3x3?4x4?7?2x1?x2?x3?2x4?3?x1,x2,x3,x4?0?
(23). 唯一最优解X*?(0,0,1,1)T,z*??3；
maxz?2x1?3x2?5x3?x1?x2?x3?7
?2x1?5x2?x3?10?x,x,x?0?123454T*102*(24). 唯一最优解X?(,,0),z?；
777（24）??2x1?4x2?5x3?x4?0?2x1?x2?4?（25）? （26） ?3x1?x2?7x3?2x4?2 ?x1?7x2?7??x,x?0?5x1?2x2?x3?6x4?15?12?x1,x2,x3,x4?0?2110T*31**T*(25). X?(,),z? ； (26). X?(3,0,0,0),z?9
131313maxz?2x1?x2?5x3?6x4（27）?minz?x1?x2minz?3x1?2x2?x3?4x4?2x1?x3?x4?8?2x1?2x2?x3?2x4?12?x1,x2,x3,x4?0?*T*
(27). 唯一最优解X?(0,0,4,4),z?44；
第 3 页 共 30 页
maxz?3x1?2x2?2.9x3?8x1?2x2?10x3?300（28）?10x?5x?8x?400
?123??2x1?13x2?10x3?420??x1,x2,x3?0(28). 唯一最优解X?(33811622T*2029,,),z?； 155315maxz?7x1?12x2?10x3*（29）??x1?x2?x3?20?2x1?2x2?x3?30?x,x,x?0?123
(29). 唯一最优解X*?(0,10,10)T,z*?220；
maxz?15x1?16x2?6x3（30）??x1?x2?x3?20?2x1?2x2?x3?30?x,x,x?0?123
(30). 唯一最优解X*?(0,15,0)T,z*?240；
maxz?x1?2x2?x3?2x1?x2?3x3?5（31）??4x?x?x?4
?123??x1?3x2?6??x1,x2,x3无正负号限制(31). 唯一最优解X?(?9119T*11,,?),z?； 4442maxz?3x1?2x2?3x3*?2x1?x2?x3?2（32）??3x1?4x2?2x3?8?x,x,x?0?123*T*
(32). 唯一最优解X?(0,2,0),z?4；
minz?2x1?x2?2x3??x1?x2?x3?4（33）?
?x?x?x?6?123?x?0,x?0,x无正负号限制23?1(33). 唯一最优解X?(?5,0,?1),z??12；
*T*第 4 页 共 30 页
maxz?x1?5x2?3x3（34）??x1?2x2?x3?3?2x1?x2?4?x,x,x?0?123
(34). 唯一最优解X*?(2,0,1)T,z*?5；
minz?2x1?2x2（35）???x1?x2?1?x1?x2??2?x,x?0?12
(35). 无可行解；
maxz?3x1?5x2?2x3?x1?2x2?2x3?14（36）?
2x?4x?3x?23?123?0?x?4,2?x?5,0?x?3123?(36). 唯一最优解X?(4,15T*123,0),z?； 44maxz?5x1?2x2?3x3*?x1?5x2?2x3?30（37）??x1?5x2?6x3?40?x,x,x?0?123*
(37). 唯一最优解X?(30,0,0),z?150；
T*maxz?x1?2x2?3x3?4x4?x1?2x2?2x3?3x4?20（38）?
2x?x?3x?2x?20?1234?x,x,x,x?0?1234*T*
(38). 唯一最优解X?(0,0,4,4),z?28；
minz?5x1?2x2?4x3?3x1?x2?2x3?4（39）?
6x?3x?5x?10?123?x,x,x?0?123(39). 唯一最优解X?(2/3,2,0),z?22/3；
*T*第 5 页 共 30 页