There are many common variations of the maximum flow problem. Here are four of them (a) There are many sources and many sinks, and we wish to maximize the total flow from all sources to all sinks. (b) Each vertex also has a capacity on the maximum flow that can enter it. (c) Each edge has not only a capacity, but also a lower bound on the flow it must carry (d) The outgoing flow from each node u is not the same as the incoming flow, but is smaller by a factor of (1- e), where e is a loss coefficient associated with node u. Each of these can be solved efficiently. Show this by reducing (a) and (b) to the original max-flow problem, and reducing (c) and (d) to linear programming