运筹学清华大学出版社(胡运权着)课后答案(.资料下载.pdf

1、运筹学教程第二版运筹学教程第二版 习题解答习题解答运筹学教程运筹学教程School of ManagementSchool of Managementpage page 2 26 January 20116 January 20111.1 用图解法求解下列线性规划问题。#并指出问 题具有惟一最优解、无穷多最优解、无界解还是无可 行解。#0,422664.32min）1（21212121xxxxxxstxxZ0,124322.23max）2（21212121xxxxxxstxxZ85105120106.max）3（212121xxxxstxxZ0,23222.65max）4（21212121xx

2、xxxxstxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 3 36 January 20116 January 2011是一个最优解无穷多最优解3,31,10,422664.32min）1（2121212121ZxxxxxxxxstxxZ该问题无解0,124322.23max）2（21212121xxxxxxstxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 4 46 January 20116 January 201116,6,1085

3、105120106.max）3（21212121ZxxxxxxstxxZ唯一最优解该问题有无界解0,23222.65max）4（21212121xxxxxxstxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 5 56 January 20116 January 20111.2 将下述线性规划问题化成标准形式。#.,0,2321422245243min）1（43214321432143214321无约束xxxxxxxxxxxxxxxxstxxxxZ无约束321321321321,0,0624322min）2（xxxxx

4、xxxxstxxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 6 66 January 20116 January 2011.,0,2321422245243min）1（43214321432143214321无约束xxxxxxxxxxxxxxxxstxxxxZ0,232142222455243max64241321642413215424132142413214241321xxxxxxxxxxxxxxxxxxxxxxxstxxxxxZ运筹学教程运筹学教程School of ManagementSchool of M

5、anagementpage page 7 76 January 20116 January 2011无约束321321321321,0,0624322min）2（xxxxxxxxxstxxxZ0,6243322max43231214323121323121323121xxxxxxxxxxxxxxstxxxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 8 86 January 20116 January 20111.3 对下述线性规划问题找出所有基解指出哪 些是基可行解并确定最优解。#6,1,0031024893631

6、223max）1（6153214321321jxxxxxxxxxxxstxxxZj）4,1（,0322274322325min）2（432143214321jxxxxxxxxxstxxxxZj运筹学教程运筹学教程School of ManagementSchool of Managementpage page 9 96 January 20116 January 20116,1,0031024893631223max）1（6153214321321jxxxxxxxxxxxstxxxZj基可行解x1x2x3x4x5x6Z03003.503001.5080300035000.7500022.252

7、.25运筹学教程运筹学教程School of ManagementSchool of Managementpage page 10106 January 20116 January 2011）4,1（,0322274322325min）2（432143214321jxxxxxxxxxstxxxxZj基可行解x1x2x3x4Z00.5205001152/5011/5043/5运筹学教程运筹学教程School of ManagementSchool of Managementpage page 11116 January 20116 January 20111.4 分别用图解法和单纯形法求解下述线

8、性规划 问题并对照指出单纯形表中的各基可行解对应图解 法中可行域的哪一顶点。#0,825943.510max）1（21212121xxxxxxstxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 12126 January 20116 January 20110,24261553.2max）2（21212121xxxxxxstxxZ运筹学教程运筹学教程School of ManagementSchool of Managementpage page 13136 January 20116 January 2011l.5

9、 上题（1）中若目标函数变为max Z=cx1+dx2 讨论c,d的值如何变化使该问题可行域的每个顶 点依次使目标函数达到最优。#解得到最终单纯形表如下Cjcd00CB基bx1x2x3x4dx23/2015/14-3/4cx1110-2/1410/35j00-5/14d+2/14c 3/14d-10/14c运筹学教程运筹学教程School of ManagementSchool of Managementpage page 14146 January 20116 January 2011当c/d在3/10到5/2之间时最优解为图中的A点当 c/d大于5/2且c大于等于0时最优解为图中的B点当c

10、/d 小于3/10且d大于0时最优解为图中的C点当c/d大于 5/2且c小于等于0时或当c/d小于3/10且d小于0时最优解 为图中的原点。#运筹学教程运筹学教程School of ManagementSchool of Managementpage page 15156 January 20116 January 2011式中1c1 3,4c2 6,-1a11 3,2a12 5,8b1 12,2a21 5,4a22 6,10b2 14,试确定 目标函数最优值的下界和上界。#0,.max21222212112121112211xxbxaxabxaxastxcxcZl.6 考虑下述线性规划问题运

11、筹学教程运筹学教程School of ManagementSchool of Managementpage page 16166 January 20116 January 2011最优值上界为210,14421221.63max21212121xxxxxxstxxZ解上界对应的模型如下c,b取大a取小运筹学教程运筹学教程School of ManagementSchool of Managementpage page 17176 January 20116 January 2011最优值下界为6.40,1064853.4max21212121xxxxxxstxxZ解下界对应的模型如下 c,b

12、取小a取大运筹学教程运筹学教程School of ManagementSchool of Managementpage page 18186 January 20116 January 2011l.7 分别用单纯形法中的大M法和两阶段法求解 下列线性规划问题并指出属哪类解。#该题是无界解。#3,1,00222623max）1（3231321321jxxxxxxxxstxxxZj运筹学教程运筹学教程School of ManagementSchool of Managementpage page 19196 January 20116 January 20116,0,54,590,623824.

13、32min）2（3212121321321ZxxxxxxxxxxstxxxZ最优解之一该题是无穷多最优解。#运筹学教程运筹学教程School of ManagementSchool of Managementpage page 20206 January 20116 January 2011517,0,1,59,524,1,042634334max）3（43214213212121ZxxxxjxxxxxxxxxstxxZj该题是唯一最优解运筹学教程运筹学教程School of ManagementSchool of Managementpage page 21216 January 20116

14、 January 2011该题无可行解。#3,1,052151565935121510max）4（321321321321jxxxxxxxxxxstxxxZj运筹学教程运筹学教程School of ManagementSchool of Managementpage page 22226 January 20116 January 20111.8 已知某线性规划问题的初始单纯形表和用单 纯形法迭代后得到下面表格试求括弧中未知数al值。#项 目X1X2X3X4X5X46（b）（c）（d）10X51-13（e）01Cj Zja-1200X1（f）（g）2-11/20X54（h）（i）11/21Cj

15、 Zj0-7jk（l）b=2,c=4,d=-2,g=1,h=0,f=3,i=5,e=2,l=0,a=3,j=5,k=-1.5运筹学教程运筹学教程School of ManagementSchool of Managementpage page 23236 January 20116 January 20111.9 若X（1）、X（2）均为某线性规划问题的最优解 证明在这两点连线上的所有点也是该问题的最优解。#也是最优解。#所以也是可行解且满足两点连线上的点对于任何满足和设XXCXCXaCaXCXaCaXCXCXaaXXXaXbAXXCZXXTTTTTTTT,）1（）1（,100max）2（）2

16、（）2（）1（）2（）1（）2（）1（）2（）1（运筹学教程运筹学教程School of ManagementSchool of Managementpage page 24246 January 20116 January 20111.10 线性规划问题max ZCX,AXbX0设 X0为问题的最优解。#若目标函数中用C*代替C后问题 的最优解变为X*求证（C*-C）（X*-X0）00）（）（）（;#0max;#0max0*00*0*00XXCXXCXXCCXCXCXCZXCXCXCXZX的最优解故是的最优解故是运筹学教程运筹学教程School of ManagementSchool of Managementpage page 25256 January 20116 January 20111.11 考虑线性规划问题0,）（75232）（24.42min432143214214321xxxxiixxxxixxxstxxxxZ模型中为参数要求（1）组成两个新的约束（i）（i）+（ii）（ii）（ii）一2（i）根据（i）（ii）以x1,x2 为基变量列出 初始单纯形表运筹学教程运筹学教程School of Manage