Network Flow Problems The purpose of this project is to show how systems of linear equations may be used to model flow through a network. Consider the problem of calculating the pattern of traffic flow for a community. The network in this case consists of a system of streets and nodes, or intersections, where the roads meet. Each street will have a certain rate of flow, measured in vehicles per some time interval. Given certain flow rates into the road system, the rates of flow on each street will be computed. There is one big assumption: at each intersection, the flow is "conserved"; that is, a car that reaches an intersection must continue through the network. For example, if the flow rates into a given intersection are x1 and 30, and the flow rates out of the same given intersection are x2 and 50, then x1 = 30 x2 50, or x1 =x2 20. Thus, each intersection produces a linear equation in the unknown rates. Solving the system of linear equations resulting from each intersection will give the flow rates over each branch. Questions: 1. Do you believe that the "big assumption" is legitimate? When might this assumption fail