Question: Consider an LP in which the variable x k is unrestricted in sign. Prove that by substituting x k = x k x

Consider an LP in which the variable x_k is unrestricted in sign. Prove that by substituting x_k = x_k⁻ − x_k⁺, where xk− and x_k⁺ are nonnegative, it is impossible that the two variables replace one another in an alternative optimum solution.

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