Problem 2. Take two functions f and F , as well as the utility function u as given. Consider the problem where we want to maaimize over the set of paths c and stopping time T 2 0 the value of: [0 ma), c(s))als + mm subject to and an initial value 513(0) = so. 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