Consider a modification to the Activity Selection problem in which each activity i has, in addition to a start time s$\_$i and finish time f$\_$i$,$ a profit p$\_$i$.$ The goal is no longer to maximize the number of activities scheduled, but instead to maximize the total profit of the activities scheduled. That is$,$ we wish to choose a set A of compatible activities such that $\_$j in A p$\_$j is maximized. Consider the following two greedy choices. For each one, determine whether it is a "safe" greedy choice for this modified Activity Selection problem. If your answer is yes, prove the "Greedy$-$choice property". If your answer is no$,$ please give a counterexample and show that the greedy choice will not lead to an optimal solution. $(1)$ Greedy choice $1$: Always select a job with the earliest finish time that is compatible with all previously selected activities. $(2)$ Greedy choice $2$: Always select a job with the highest pro t per time unit $($i$.$e$.,.$p$\_$i $/($f$\_$i$-$s$\_$i$))$ that is compatible with all previously selected activities.