Consider the problem: Minimize ex subject to Ax 2 b, x 20. Let x* be an...

 

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Consider the problem: Minimize ex subject to Ax 2 b, x 20. Let x* be an optimal solution. Suppose that A is decomposed into [A] and b is decomposed A₂ into such that A₁x* = b₁ and A₂x* >b₂. Show that x* is also an optimal solution to the problem: Minimize ex subject to A₁x ≥ b₁, x ≥ 0, and to the problem: Minimize ex subject to A₁x = b₁, x ≥ 0. Consider the problem: Minimize ex subject to Ax 2 b, x 20. Let x* be an optimal solution. Suppose that A is decomposed into [A] and b is decomposed A₂ into such that A₁x* = b₁ and A₂x* >b₂. Show that x* is also an optimal solution to the problem: Minimize ex subject to A₁x ≥ b₁, x ≥ 0, and to the problem: Minimize ex subject to A₁x = b₁, x ≥ 0.