For each problem listed below:

• Hand in a complete algebra formulation, including clear definitions for all variables.  You may skip any algebraic simplifications that might arise.
• Create an Excel spreadsheet model of the problem and find an optimal solution with Solver.  Hand in the standard printouts.
   

 Q1.  (30 points)  Your company has eight retail stores in the mid-Atlantic region: Cherry Hill, Exton, Lawrence, Menlo Park, Neshaminy, Short Hills, Sparta, and Wallville.  You have decided to build some regional distribution centers to supply goods to these stores, and have identified five possible locations, as follows (annual operating costs are in millions of dollars):

Which distribution centers should you build so as to minimize total annual operating cost, while making sure that for every store, there is at least one distribution center that is "close enough"?
 

Q2.  (35 points) Your firm has $11 million to spend on new product development.  You have identified 7 possible products, code-named A through G.  The development cost and estimated NPV of making and selling the products are as follows (all numbers are in millions of dollars):

You cannot develop product C unless you also develop B, and you cannot develop E unless you develop B and D.  Also, you must develop at least two products from the set {A,B,C}, and at most 3 products from the set {C,D,E,F,G}.  Which products should you develop in order to maximize your expected NPV?  Note that the NPV given is already net of the development cost.

Q3.  (35 points)  Problem 49 on page 161 of the course pack (State University computer purchasing).  Note that if you decide not to purchase any computers from a vendor, then you do not have to pay the delivery charge, and your total cost for that vendor is $0.