Problem on network models

Question

Assignment:

Q1. The west-to-east air traffic system passing through the United States can handle aircraft flows with capacities in hundreds of planes per hour as shown.  What is the peak air traffic load (From city 1 to city 5) in aircraft per hour that this system can handle?

	To
From	1	2	3	4	5
1	-	2	-	4	-
2	1	-	2	3	3
3	2	2	-	5	2
4	-	-	-	-	3
5	-	2	2	1	-

Q2.  Find the shortest route from Node 1 to each of the other nodes in the transportation network represented below.

Route From Node	Distance
1 to 2	50
1 to 3	100
2 to 3	75
2 to 5	60
3 to 4	80
3 to 5	70
3 to 6	65
4 to 6	200
5 to 6	150

Q3. As part of the planning for a major office development project, it is necessary to install telephone lines to the buildings.  Information about the project is given below. The distances are provided in hundreds of feet.  Which offices should be connected so that total wiring costs (i.e., total distance) are minimized?  What is the total length of this?

Buildings	Distances (100s ft)
1 to 2	4
1 to 3	3
1 to 4	2
2 to 4	4
3 to 5	1
3 to 6	5
4 to 5	3
4 to 7	3
5 to 7	2
6 to 7	6

Q4. Brantley College has decided to "wire" their campus.  The first stage in this effort is to install the "backbone," i.e., to connect all the buildings.  The table below gives the distances between the various buildings on campus in hundreds of feet.  How should the buildings be connected to minimize the total length of cable?  What length of cable is required?

Distances in Hundreds of Feet
From	To
	Building  1	Building  2	Building  3	Building  4	Building  5	Building  6
Building 1		3	7	5	5	4
Building 2			5	2	6	6
Building 3				5	4	4
Building 4					5	3
Building 5						4
Building 6

Provide complete and step by step solution for the question and show calculations and use formulas.