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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�12page26January2011SchoolofMa
2、nagement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�1612maxZ�5x�6x12�2x�x�212(4)�st.��2x1�3x2�2�x,x�0�12该问
3、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�123page56January2011SchoolofManagement运筹学教程minZ��3x�4x�2x�5x1234�4x1�x2�2x3�
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5、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�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�
6、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xxxxxxZ12345603003.503001.5080300035000.7500022.252.25page96January2011SchoolofManagement运筹学教程minZ�5x�2x�3x�2x1234�x�2x�3x�4x�71234(2)�st�2x1�2x2�x3�2x4�3�x
7、�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