Shortest Path Problems with Losses) Consider the shortest path-like problem of Exercise 2.31 where a vehicle wants to go on a forward path from an origin node 1 to a destination node t in a graph with no forward cycles, and for each arc there is a given probability that the vehicle will be destroyed in crossing the arc. Formulate the problem as a network flow problem with gains. Provide conditions under which your formulation makes sense when the graph has some forward cycles and the arc lengths are nonnegative.