Hope you guys don't mind me asking another question (this one is a bit lengthy). I'm mostly confused by the wording of the question and what its actually asking me to do.
1. The Houndsworth Town Sports Association is planning a sports carnival. Traffic through the town will be diverted around the sporting venues during the carnival. The network (attached below) shows the road that can be used during the carnival represented by the edges and intersection of those roads shown as vertices.
The number on the edges are the maximum number of cars that can travel on the road each hour. The roads will be restricted to allow one-way traffic only, as shown by the arrows.
a. How many cars per hour can enter the diversion roads?
I'm guessing this is just asking from A - B, thus 180? But correct me if I'm wrong.
One cut (Cut 1) is shown on the diagram above.
b. i. If the capacity of Cut 1 is 150, what is the value of m?
ii. Show that the smallest value of m that will ensure there will be no build-up of cars at intersection B is 50.
The capacity of the road between intersection B and intersection E is 50 (m = 50). The maximum flow through the network is currently 150 cars per hour.
c. Mark in the cut that determines the maximum flow on the network above.
I don't quite understand how m = 50? I thought it would just be 150-130=20.
The Sport Association have noticed that there could be a build-up of traffic at intersection E and F.
d. If the road between intersections F and H was improved, what is the maximum capacity is should take to the solve the potential traffic build-up at F?
In order to solve the potential build-up of traffic at intersection E, the Sports Association open another road from intersection E to intersection D.
e. i. What is the minimum capacity of this road that will avoid traffic build-up at intersection E?
ii. Explain why a road between intersection E and D cannot solve potential traffic build-up in the network.
Super sorry for the incredibly lengthy question, I'm just really confused about what the hell its asking me to do and how to go about getting there.
1. a. I think you're right but not 100% sure.
b. i. You're right, the answer is 30
ii. The inflow to node B is 180 which comes from the source, which means to prevent congestion the outflow cannot exceed 180. We already have 90+40=130 so m has to be maximum of 50 so that the cut doesn't exceed 180.
c. The cut goes through 30, 40 and 80.
d. The inflow is 100 and the outflow is only 80 which is 20 less. So we should increase it to 100.
e. i. The inflow is 50 and the outflow is only 30 which is 20 less. So the new road from E to D should be at least 20.
ii. I think it's because there's still some congestion at other intersections in the network, for example the outflow of C is 100 which exceeds its inflow of 90. Not 100% sure.
Hope I helped.