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Linear Programming: Largest possible adjacent basic feasible solutions

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For a given basic feasible solution in a problem in standard form with no degenerate extreme points, what is the largest possible number of adjacent basic feasible solutions that it can have, as a function of n and m?

Give an example of when it will be strictly fewer than this number.

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For a given basic feasible solution in a problem in standard form with no degenerate extreme points, what is the largest possible number of adjacent basic feasible solutions that it can have, as a function of n and m?

Suppose we have m independent constraints, and ...

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