For each problem below, hand in an algebra formulation, and also solve using Excel and Solver, handing 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?
 

Q3. (35 points)  Problem 55 on page 163 of the course pack (Monsanto).  Assume that you must produce at least 359 million pounds of the product -- that is, production of  more than 359 million pounds is permissible.  You are also allowed to leave any reactor off for the entire year, in which case its cost is $0 and it produces 0 pounds of the product.