2. The following figure shows the flow of traffic near a city's center during the rush hours on a typical week days. Each road can handle a maximum of 1000cars/hour without causing congestion. The flow of traffic is controlled by traffic lights at each of the five intersections.
(a) Setup a system of linear equations describing the traffic flow.
(b) Solve the system devised in part (a) and suggest two possible traffic flow patterns that will ensure no traffic congestion.
(c) Suppose 7th Avenue between 3rd and 4th street soon to be closed for road repairs. Find one possible flow pattern that will result in a smooth flow of traffic.