4. Consider the follow map of one-way streets (direction given by the blue arrows). The average hourly volume of traffic entering or leaving this map on a Sunday are given

by the constants (in upper case). Let x1'''''''' xe,be the average volume of traffic along the road segments in the map. At each intersection (I to V), the number of automobiles entering the intersection must equal the number of automobiles leaving. For example, at interection I, we have A+x1 = 3 (b) Write a system of five equations in variables z1,.., Ta corresponding to the Intersections I to (e) Solve the system of equations in Part (b). (d) Determine the smallest possible average volume (r4) along the highlighted road segment on a Sunday.Explain how you arrive at your answer. (e) If the highlighted road segment has a capacity of 50 cars, determine the largest possible average volume(T4) on a Sunday. Explain how you arrive at your answer.