Assignment Problems:

1. A manufacturer purchases 6000 cases of a certain component for $100 per case from two suppliers: Supplier A and Supplier B.

Supplier A is currently responsible for 1/2 of the total demand.  The two suppliers currently pay $2 per case for transportation and achieve the same average delivery time of 10 days.

However, for each day that a supplier can reduce in the average delivery time, the manufacturer is willing to shift 5% of its total purchase to the supplier offering the premium service. A supplier earns a margin of 25% of the selling price on each case before transportation cost kicks in.

a) How much profit does Supplier A make currently? Please provide at least one step of calculation and the correct answer for full credit.

b) Suppose Supplier A is willing to reduce its average delivery time by 3 days and the transportation rate increases by $0.5 per case for each dayreduced in the average delivery time. How much profit can Supplier A make by offering the premium transportation service? Assume that Supplier B take no action. Please provide the new sales number, at least one step of calculation, and the correct answer for full credit.

2. a) Please cite an example of a company that uses multiple distribution channels to distribute its products and use one or two sentences to support your choice. 

b) Please cite an example of a company that adopts corporate vertical marketing system in its distribution and use one or two sentences to support your choice. 

c) Please cite an example of a company that adopts administered vertical marketing system in its distribution and use one or two sentences to support your choice. 

3. The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub.

Using the Centroid method, at what map coordinates should the central hub be located? Please provide at least one step of calculation for each of the two coordinates of the centroid for full credit.