Homework 9
1) The north- south highway system passing through Albany, New York, can accommodate the capacities shown below (not drawn to scale). Note: Node 2 to node 5 is one- way.
a) Can the highway system accommodate a north- south flow of 10,000 vehicles per hour?
b) What is the maximum number of vehicles the highway system can accommodate?
c) How many vehicles per hour must travel along each arc (branch) to obtain this maximal flow? List each branch from start node to end node and list the number of vehicles on that branch.
d) Proposed road construction projects will change the north- south highway system as indicated below. How many more vehicles will the proposed changes accommodate?
2) Morgan Trucking Company operates a special pickup and delivery service between Chicago and six other cities located in neighboring states. When Morgan receives a request for service, it dispatches a truck from Chicago to the city requesting service as soon as possible. With both fast service and minimum travel costs as objectives for Morgan Trucking, it is important that the truck take the shortest route from Chicago to the specified city. Assume that the following network (not drawn to scale) with distances given in miles represents the highway network for this problem.
a) What path should be taken by drivers to travel from node 1 to node 7?
b) How many miles will the driver travel taking the route in part a)?
c) Assume that because of congestion that the driver averages 45 mph, how long will it take the driver to travel from node 1 to node 7?
3) A small construction firm is building a subdivision of houses and needs to connect each house to the waste water system for the county. The county will connect the waste water system to house 4. The cost (in thousands) of connecting each house in the subdivision is given in the network below (not drawn to scale).
a) What is the lowest cost to connect all of the houses?
b) Which of the following possible connections will not be used? Not all connections listed.
| House 1 | House 2 |
| House 2 | House 7 |
| House 3 | House 7 |
| House 5 | House 7 |
| House 6 | House 7 |
| House 7 | House 9 |
| House 7 | House 8 |
| House 8 | House 9 |
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