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Advanced Proof

Proof of Validity for Gomory Fractional Cuts

Students often struggle to see why fijxj f_{ij} x_j doesn't exclude integer points. Crucially, the cut relies on xj0 x_j \geq 0 and the fact that fi>0 f_i > 0 ; any integer point that satisfies the original constraints will automatically satisfy the inequality, leaving the feasible set intact while pruning the non-integer vertex.
Institutional Reference: Linear and Integer Programming
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