The downtown core of Gotham City consists of one-way streets, and the traffic flow has b...

The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in Figure 2.19, the numbers represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours.

(a) Set up and solve a system of linear equations to find the possible flows f₁, . . . , f₄.

(b) If traffic is regulated on CD so that f₄ = 10 vehicles per minute, what will the average flows on the other streets be?

(c) What are the minimum and maximum possible flows on each street?

(d) How would the solution change if all of the directions were reversed?