For a standard form linear program that minimizes an objective function as follows:$$ \begin{aligned} \text{minimize } &c^T x \\ \text{subject to } & Ax =0, x \ge 0 \end{aligned} $$
a degenerate basic feasible solution can be optimal even when some reduced costs are positive.
Page 87 of the book Introduction to Linear Programming[1], the author mentioned:
On the other hand, in the degenerate case, having an optimal basic feasible solution does not necessarily mean that the reduced costs are nonnegative.
However, I can't imagine such a case. What is an example of this?
[1] Bertsimas, Dimitris, and John N. Tsitsiklis. Introduction to linear optimization. Vol. 6. Belmont, MA: Athena Scientific, 1997.
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