A flow network with demands is a directed capacitated graph with potentially multiple sources and sinks, which may have incoming and outgoing edges respectively. In particular, each node v V has an integer demand dv; if dv > 0, v is a sink, while if dv < 0, it is a source. Let S be the set of source nodes and T the set of sink nodes. A circulation with demands is a function f : E R+ that satisfies (a) capacity constraints: for each e E, 0 f(e) ce. (b) demand constraints: For each v V , f in(v) f out(v) = dv. We are now concerned with a decision problem rather than a maximization one: is there a circulation f with demands that meets both capacity and demand constraints? i. Derive a necessary condition for a feasible circulation with demands to exist. ii. Reduce the problem of finding a feasible circulation with demands to Max Flow.