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mathematical optimization - Caveats of LinearProgramming on Integers domain


When using LinearProgramming with the Integers domain, Mathematica issues the following warning:


In[3]:= LinearProgramming[{1, 1}, {{5, 2}}, {3}, Automatic, Integers]

During evaluation of In[3]:= LinearProgramming::lpip: Warning: integer linear programming will use a machine-precision approximation of the inputs.


Out[3]= {1, 0}


Warning: integer linear programming will use a machine-precision approximation of the inputs.



I am not deeply familiar with integer programming. What are the practical implications of using a "machine-precision approximation"? I assume that this means is that the result may not be exact (optimal). Under what circumstances will this be the case, and how might one go about detecting it? Are there alternative functions in Mathematica which can avoid these issues?




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