$15\mathrm{.}1-2$ Show, by means of a counterexample, that the following "greedy" strategy does not always determine an optimal way to cut rods. Define the density of a rod of length i to be pi$/$i$,$ that is$,$ its value per inch. The greedy strategy for a rod of length n cuts off a first piece of length i$,$ where $1$ s i $,$ having maximum density. It then continues by applying the greedy strategy to the remaining piece of length n $-$i