Question: Suppose you are given a directed graph G = (V, E), with positive integer capacity c_e on each edge e. You are also given a

Suppose you are given a directed graph G = (V, E),

Suppose you are given a directed graph G = (V, E), with positive integer capacity c_e on each edge e. You are also given a set of sources s_1. ....., s_n and a set of sinks t_1, ..., t_m. Each source s_i has a supply of up to S_i amount of flow that can be sent out from it, and each sink t_j has a demand D_j for flow that it receives. Design a polynomial time algorithm to determine whether it is possible to design a flow that meets all demands of all sinks subject to the supplies of the sources

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