Sufficient condition for extending $x$ to a feasible solution of (RC): $\sum_ja_{ij}x_j+\epsilon\beta_i(x)\le b_i^+$

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Sufficient condition for extending $x$ to a feasible solution of (RC): $\sum_ja_{ij}x_j+\epsilon\beta_i(x)\le b_i^+$ · Prove2Me