points$]$ We say that a problem exhibits the optimal substructure property when optimal solutions to a problem incorporate optimal solutions to related subproblems, which we may solve independently. Suppose that in the rod$-$cutting problem, we also had limit I, on the number of pieces of length i that we are allowed to produce, for $i=1,2,$dots,$n.$ Show that the optimal$-$ substructure property described no longer holds. $($Ex$.15\mathrm{.}3-5)$

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