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1、运运筹筹学学教教程程��第第二二版版��习习题题解解答答运筹学教程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最优解、无穷多最优解、无界解还是无可行解。minZ�2x�3xmaxZ�3x�2x1212�4x1�6x2�6�2x1�x2�2(1)�(2)�st.�2x1�2x2�4st.�3x1�4x2�12��x,x�0x,x�0�12�12maxZ�x�xmaxZ�5x�6x1212�6x1�10x2�120�2x1�x2�2(3)�(4)�st.�5�x1�10st.��2x1�3x2�2��5�x�8x,x�0�2�12pa
2、ge26January2011SchoolofManagement运筹学教程minZ�2x�3x12�4x1�6x2�6(1)�st.�2x1�2x2�4�x,x�0�12无穷多最优解�1x�1,x�,Z�3是一个最优解123maxZ�3x�2x12�2x�x�212(2)�st.�3x1�4x2�12�x,x�0�12该问题无解page36January2011SchoolofManagement运筹学教程maxZ�x�x12�6x1�10x2�120(3)�st.�5�x1�10�5�x�8�2唯一最优解�x�10,x�6,Z�1612
3、maxZ�5x�6x12�2x�x�212(4)�st.��2x1�3x2�2�x,x�0�12该问题有无界解page46January2011SchoolofManagement运筹学教程1.2将下述线性规划问题化成标准形式。minZ��3x�4x�2x�5x1234�4x1�x2�2x3�x4��2�(1)�x1�x2�x3�2x4�14st�.�2x�3x�x�x�2�1234�x,x,x�0,x无约束�1234minZ�2x�2x�3x123��x1�x2�x3�4(2)�st��2x1�x2�x3�6�x�0,x�0,x无约束�1
4、23page56January2011SchoolofManagement运筹学教程minZ��3x�4x�2x�5x1234�4x1�x2�2x3�x4��2�(1)�x1�x2�x3�2x4�14st�.�2x�3x�x�x�2�1234�x,x,x�0,x无约束�1234maxZ�3x�4x�2x�5x�5x1234142��4x�x�2x�x�x�21234142��x1�x2�x3�2x41�2x42�x5�14st��2x�3x�x�x�x�x�2�12341426�x,x,x,x,x,x�0�12341426page66Jan
5、uary2011SchoolofManagement运筹学教程minZ�2x�2x�3x123��x1�x2�x3�4(2)�st��2x1�x2�x3�6�x�0,x�0,x无约束�123maxZ�2x�2x�3x�3x123132��x1�x2�x31�x32�4�st�2x1�x2�x31�x32�x4�6�x,x,x,x,x�0�1231324page76January2011SchoolofManagement运筹学教程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�并确定最优解。maxZ�3x�x�2x123�12x�
6、3x�6x�3x�91234�(1)�8x1�x2�4x3�2x5�10st�3x�x�0�16�x�0�,j�1,�,6��jminZ�5x�2x�3x�2x1234�x�2x�3x�4x�71234(2)�st�2x1�2x2�x3�2x4�3�x�0,(j�1,�4)�jpage86January2011SchoolofManagement运筹学教程maxZ�3x�x�2x123�12x�3x�6x�3x�91234�(1)�8x1�x2�4x3�2x5�10st�3x�x�0�16�x�0�,j�1,�,6��j基可行解xxxxxx
7、Z12345603003.503001.5080300035000.7500022.252.25page96January2011SchoolofManagement运筹学教程minZ�5x�2x�3x�2x1234�x�2x�3x�4x�71234(2)�st�2x1�2x2�x3�2x4�3�x�0,(j�1,�4)�j基可行解xxxxZ123400.5205001152/5011/5043/5page106January2011SchoolofManagement运筹学教程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
8、纯形表中的各基可行解对应图解法中可行域的哪一顶点。maxZ�10x�5x12�3x1�4x2�9(1)�st.�5x1�2x2�8�x,x�0�12page116January2
