Problem 2. Talce two functions f and F, as well as the utility function u as given. Consider the problem where we want to maximize over the set of paths c and.r stopping time T 2 0 the value of: T j; was), ctsts + FWD subject to and an initial value 113(0) : 3:. In class we found the equation characterizing the value function which is solution of this problem when T cannot be chosen and is T : +00 and . Derive the equation characterizing the value function which is solution of this