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Prove that if p is an lplinear programming in standard form

Prove that if P is an LP(linear programming) in standard form, P has an optimal solution, and P has no degenerate optimal solutions, then there is a unique optimal solution to the dual of P. You can assume that the matrix A is full rank. (Hint: Use the complementary slackness condition and the fact that if an LP in standard form has an optimal solution, then it has no optimal basic feasible solution)

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Mathematics: Prove that if p is an lplinear programming in standard form

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