2. Traffic Flow Consider the following scenario. You are on a city planning committee and must decide how to control the flow of traffic in a particular residential neighbourhood. At each intersection, you have to decide whether to install a 4-way stop, a roundabout, or an uncontrolled intersection (in an uncontrolled intersection, the streets intersect without signs, roundabouts or other traffic controls). There are several restrictions in how the intersections can be controlled. The figure below gives an overview of the neighbourhood. The red stars indicate the 8 intersections under consideration. The intersection nearest the school in the NW corner of the neighbourhood must contain a 4-way stop for safety reasons. Along the east side of the neighbourhood runs a truck route, and no roundabouts can be placed on this street because they pose a problem for large trucks. Also, it is not allowed to have 4-way stops at consecutive intersections or to have two consecutive uncontrolled intersections. Finally, due to the cost of installing roundabouts compared with the other options, each block can have at most one of its four corners with a roundabout