The maximum flow problem was first formulated in 1954 by T.E. Harris and F.S. Ross as a simplified model of soviet Railway traffic flow1. In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm for calculating the maximum flow, the Ford-Fulkerson algorithm2. It was in 1951 when the American mathematician, George Dantzig put forward the network simplex algorithm to solve mininimum cost flow problem. We take a typical example and find the maximum flow and minimum cost. Finally we generalise The Producer’s Problem based on some assumptions and find the maximum flow and minimum cost in it. We observe that the minimum unit cost in The Producer’s Problem increases with the number of items produced increases, in contrast to natural expectation.