运筹学习题答案(第二章)2VIP免费

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SchoolofManagementSchoolofManagementpagepage22December25,2024December25,2024第二章习题解答第二章习题解答2.1写出下列线性规划问题的对偶问题。无约束321321321321321,0,,534332243422min)1(xxxxxxxxxxxxstxxxZ无限制对偶问题321321321321321,0,0433424322532max:yyyyyyyyyyyystyyyW运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage33December25,2024December25,2024第二章习题解答第二章习题解答0,0,,8374335522365max)2(321321321321321xxxxxxxxxxxxstxxxZ无约束0,0,3332675254835max321321321321321yyyyyyyyyyyystyyyW无约束对偶问题：运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage44December25,2024December25,2024.),,1,,,1(0),,1(),,1(min)3(1111njmixnjbxmiaxstxcZijnijijnjiijminjijij第二章习题解答第二章习题解答mniynjmicyystybyaWiijmjiminjmjjii,,1),,1,,,1(.max11无限制，对偶问题：运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage55December25,2024December25,2024）无约束（nnjxnnjxmmmibxammibxastxcZjjnjijijnjijijmjjj,,1),,,,1(0),,2,1(),,1(max)4(11111111第二章习题解答第二章习题解答运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage66December25,2024December25,2024）无约束（对偶问题：mmjymiynnnjcyanjcyastybybybWiimijiijmijiijmm,,1),,1(0),,2,1(),,2,1(min11111112211第二章习题解答第二章习题解答运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage77December25,2024December25,20242.2判断下列说法是否正确，为什么?(1)如果线性规划的原问题存在可行解，则其对偶问题也一定存在可行解；答：不对！如原问题是无界解，对偶问题无可行解。(2)如果线性规划的对偶问题无可行解，则原问题也一定无可行解；答：不对！道理同上。第二章习题解答第二章习题解答运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage88December25,2024December25,2024(3)在互为对偶的一对原问题与对偶问题中，不管原问题是求极大或极小，原问题可行解的目标函数值一定不超过其对偶问题可行解的目标函数值；答：不对！如果原问题是求极小，结论相反。(4)任何线性规划问题具有惟一的对偶问题。答：结论正确！第二章习题解答第二章习题解答运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage99December25,2024December25,2024第二章习题解答第二章习题解答2.3已知某求极大化线性规划问题用单纯形法求解时的初始单纯形表及最终单纯形表如下表所示，求表中各括弧内未知数的值。解：l=1,k=0,h=-1/2,a=2,c=3,b=10,e=5/4,f=-1/2,d=1/4,g=-3/4,i=-1/4,j=-1/4运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage1010December25,2024December25,2024Cj→322000CB基bX1X2X3X4X5X60X1(b)1111000X215(a)120100X3202(c)1001Cj－Zj322000┆┆┆┆┆┆┆┆┆0X45/400(d)(l)-1/4-1/43X125/410(e)03/4(i)2X25/201(f)0(h)1/2Cj－Zj0(k)(g)0-5/4(j)运筹学教程运筹学教程SchoolofManagementSchoolofManagementpagepage1111December25,2024December25,20242.4给出线性规划问题)4,,1(,0332232.6532min432143214321jxxxxxxxxxstxxxxZj(1)写出其对偶问题；(2)用图解法求解对偶问题；(3)利用(2)的结果及根据对偶问题性质写出原问题最优解。第二章习题解答第二章习题解答运筹学教程运筹学教程Schoolo...