Consider the machine replacement example Exercise 6, in which all costs (C_{i}, i=1, ldots, 6) are replaced

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Consider the machine replacement example Exercise 6, in which all costs \(C_{i}, i=1, \ldots, 6\) are replaced by \(b \cdot C_{i}\), where \(b\) is a positive constant. Show that the policy that replaces the current machine if its condition is 3 or worse is still optimal for this new problem.

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