1. Suppose that the DoT is planning to widen roads that create a bottleneck in the flow of traffic. As such, you pose this problem as a max flow/min cut problem. You have determined that roads are in need of widening if the traffic flow on the roads is at maximum capacity; these roads are essentially the bottlenecks of the road system. These bottleneck roads can be identified using the Max Flow/Min Cut theorem.

1. Using the graph representation of the road system, explain how the Max Flow/Min Cut theorem can be used to identify the bottleneck roads.

2. Create an example graph one might use to analyze this network as a Max Flow problem. Include at least 8 nodes and 16 edges. Include capacities and flows and identify the max flow and/or min cut.