运筹学清华大学出版社(胡运权着)课后答案(.资料下载.pdf

运筹学清华大学出版社(胡运权着)课后答案(.资料下载.pdf

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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SchoolofManagementSchoolofManagementpagepage226January20116January20111.1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（21212121xxxxxxstxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage336January20116January2011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SchoolofManagementSchoolofManagementpagepage446January20116January201116,6,1085105120106.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SchoolofManagementSchoolofManagementpagepage556January20116January20111.2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（xxxxxxxxxstxxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage666January20116January2011.,0,2321422245243min）1（43214321432143214321无约束xxxxxxxxxxxxxxxxstxxxxZ0,232142222455243max64241321642413215424132142413214241321xxxxxxxxxxxxxxxxxxxxxxxstxxxxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage776January20116January2011无约束321321321321,0,0624322min）2（xxxxxxxxxstxxxZ0,6243322max43231214323121323121323121xxxxxxxxxxxxxxstxxxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage886January20116January20111.3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。

@#@6,1,0031024893631223max）1（6153214321321jxxxxxxxxxxxstxxxZj）4,1（,0322274322325min）2（432143214321jxxxxxxxxxstxxxxZj运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage996January20116January20116,1,0031024893631223max）1（6153214321321jxxxxxxxxxxxstxxxZj基可行解x1x2x3x4x5x6Z03003.503001.5080300035000.7500022.252.25运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage10106January20116January2011）4,1（,0322274322325min）2（432143214321jxxxxxxxxxstxxxxZj基可行解x1x2x3x4Z00.5205001152/5011/5043/5运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage11116January20116January20111.4分别用图解法和单纯形法求解下述线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SchoolofManagementSchoolofManagementpagepage12126January20116January20110,24261553.2max）2（21212121xxxxxxstxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage13136January20116January2011l.5上题

（1）中若目标函数变为maxZ=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+2/14c3/14d-10/14c运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage14146January20116January2011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/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SchoolofManagementSchoolofManagementpagepage15156January20116January2011式中1c13,4c26,-1a113,2a125,8b112,2a215,4a226,10b214,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筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage16166January20116January2011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SchoolofManagementSchoolofManagementpagepage17176January20116January2011最优值下界为6.40,1064853.4max21212121xxxxxxstxxZ解下界对应的模型如下c,b取小a取大运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage18186January20116January2011l.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SchoolofManagementSchoolofManagementpagepage19196January20116January20116,0,54,590,623824.32min）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SchoolofManagementSchoolofManagementpagepage20206January20116January2011517,0,1,59,524,1,042634334max）3（43214213212121ZxxxxjxxxxxxxxxstxxZj该题是唯一最优解运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage21216January20116January2011该题无可行解。

@#@3,1,052151565935121510max）4（321321321321jxxxxxxxxxxstxxxZj运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage22226January20116January20111.8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）01CjZja-1200X1（f）（g）2-11/20X54（h）（i）11/21CjZj0-7jk（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SchoolofManagementSchoolofManagementpagepage23236January20116January20111.9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（）2（）1（）2（）1（）2（）1（）2（）1（运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage24246January20116January20111.10线性规划问题maxZCX,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SchoolofManagementSchoolofManagementpagepage25256January20116January20111.11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SchoolofManage