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Difference between simplex integer and rational solution

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Is there any difference between simplex  integer and rational solution when it comes to apply simplex algorithm? I am trying to solve 2023 and 2022 rational solution by pivoting x0 but my results are different. Any leads?
in * TF "Emb. Sys. and Rob." by (440 points)

1 Answer

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Of course there is a difference. The simplex algorithm as it is just computes a rational solution. You then have to strengthen the constraints of the non-integer solutions. Note that an inequality system may have rational, but no integer solutions.
by (170k points)

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