Consider the network of one-way streets in downtown Lineapolis shown in Figure 1. The numbers indicate the typical peak hour traffic flow along each road in or out of the city centre, in cars per minute, recently measured by Lineapolis council. 51 33 ? 51 37 36 FIGURE 1. Traffic flow in downtown Lineapolis. We assume that there is no build up of cars at any intersection (marked by the dots): the amount of traffic flowing in is balanced by the amount of traffic flowing out. Set up a system of equations describing the flow of traffic through each section of the streets in downtown Lineapolis, and solve to express the traffic flow in terms of any free variables. Include any constraints on any free variable to ensure legal traffic flow.