74运筹学清华大学出版社(胡运权著)课后答案(全)

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SchoolofManagementSchoolofManagementpagepage226January20116January2011第一章习题解答第一章习题解答1.1用图解法求解下列线性规划问题。并指出问题具有惟一昀优解、无穷多昀优解、无界解还是无可行解。0,422664.32min)1(21212121xxxxxxstxxZ0,124322.23max)2(21212121xxxxxxstxxZ85105120106.max)3(212121xxxxstxxZ0,23222.65max)4(21212121xxxxxxstxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage336January20116January2011第一章习题解答第一章习题解答是一个昀优解无穷多昀优解，3,31,10,422664.32min)1(2121212121ZxxxxxxxxstxxZ该问题无解0,124322.23max)2(21212121xxxxxxstxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage446January20116January2011第一章习题解答第一章习题解答16,6,1085105120106.max)3(21212121ZxxxxxxstxxZ唯一昀优解，该问题有无界解0,23222.65max)4(21212121xxxxxxstxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage556January20116January2011第一章习题解答第一章习题解答1.2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第一章习题解答第一章习题解答.,0,,2321422245243min)1(43214321432143214321无约束xxxxxxxxxxxxxxxxstxxxxZ0,,,,,232142222455243max64241321642413215424132142413214241321xxxxxxxxxxxxxxxxxxxxxxxstxxxxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage776January20116January2011第一章习题解答第一章习题解答无约束321321321321,0,0624322min)2(xxxxxxxxxstxxxZ0,,,,6243322max43231214323121323121323121xxxxxxxxxxxxxxstxxxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage886January20116January2011第一章习题解答第一章习题解答1.3对下述线性规划问题找出所有基解，指出哪些是基可行解，并确定昀优解。）（6,,1,0031024893631223max)1(6153214321321jxxxxxxxxxxxstxxxZj)4,1(,0322274322325min)2(432143214321jxxxxxxxxxstxxxxZj运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage996January20116January2011第一章习题解答第一章习题解答）（6,,1,0031024893631223max)1(6153214321321jxxxxxxxxxxxstxxxZj基可行解x1x2x3x4x5x6Z03003.503001.5080300035000.7500022.252.25运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage10106January20116January2011第一章习题解答第一章习题解答)4,1(,0322274322325min)2(432143214321jxxxxxxxxxstxxxxZj基可行解x1x2x3x4Z00.5205001152/5011/5043/5运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage11116January20116January2011第一章习题解答第一章习题解答1.4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SchoolofManagementSchoolofManagementpagepage12126January20116January2011第一章习题解答第一章习题解答0,24261553.2max)2(21212121xxxxxxstxxZ运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage13136January20116January2011第一章习题解答第一章习题解答l.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昀优。解：得到昀终单纯形表如下：Cj→cd00CB基bx1x2x3x4dx23/2015/14-3/4cx1110-2/1410/35j00-5/14d+2/14c3/14d-10/14c运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage14146January20116January2011第一章习题解答第一章习题解答当c/d在3/10到5/2之间时昀优解为图中的A点；当c/d大于5/2且c大于等于0时昀优解为图中的B点；当c/d小于3/10且d大于0时昀优解为图中的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时昀优解为图中的原点。运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage15156January20116January2011第一章习题解答第一章习题解答式中，1≤c1≤3,4≤c2≤6,-1≤a11≤3,2≤a12≤5,8≤b1≤12,2≤a21≤5,4≤a22≤6,10≤b2≤14,试确定目标函数昀优值的下界和上界。0,.max21222212112121112211xxbxaxabxaxastxcxcZl.6考虑下述线性规划问题：运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage16166January20116January2011第一章习题解答第一章习题解答昀优值（上界）为：210,14421221.63max21212121xxxxxxstxxZ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第一章习题解答第一章习题解答昀优值（下界）为：6.40,1064853.4max21212121xxxxxxstxxZ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SchoolofManagementSchoolofManagementpagepage18186January20116January2011第一章习题解答第一章习题解答l.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(3231321321jxxxxxxxxstxxxZj运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage19196January20116January2011第一章习题解答第一章习题解答6,0,54,590,623824.32min)2(3212121321321ZxxxxxxxxxxstxxxZ昀优解之一：该题是无穷多昀优解。运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage20206January20116January2011第一章习题解答第一章习题解答517,0,1,59,524,,1,042634334max)3(43214213212121ZxxxxjxxxxxxxxxstxxZj该题是唯一昀优解：）（运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage21216January20116January2011第一章习题解答第一章习题解答该题无可行解。）（3,,1,052151565935121510max)4(321321321321jxxxxxxxxxxstxxxZj运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage22226January20116January2011第一章习题解答第一章习题解答1.8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a∼l值。项目X1X2X3X4X5X46(b)(c)(d)10X51-13(e)01Cj－Zja-1200X1(f)(g)2-11/20X54(h)(i)11/21Cj－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SchoolofManagementSchoolofManagementpagepage23236January20116January2011第一章习题解答第一章习题解答1.9若X(1)、X(2)均为某线性规划问题的昀优解，证明在这两点连线上的所有点也是该问题的昀优解。也