American Soy, a medium sized distributor of soy products supplies a number of small retail sores in 10 towns spread out across 10 towns along the Eastern seaboard. It is considering setting up new facilities to better service its customers and will build processing facilities in some of the towns listed in the table below. The new processing facilities will also service other towns that do not have the same facility set up. A processing facility can service every town within a 300-mile radius. American Soy wants to keep its costs at or below its budgeted $900,000.00. Jim, the Operations Manager has been tasked with constructing the minimum number of processing facilities that will enable it to service all towns it currently services.

The table below lists all towns within a 300-mile radius of every town. It also lists the expected fixed cost for a processing facility in each town:

a) Formulate an integer programming model for this problem and solve it in MS Excel using SOLVER.

b) What would the solution be if you remove the cost constraint from the model formulation in part (a) above?

c) What is the difference in cost?

City Cities within 300 Miles) Expected Fixed Costs ($1,000s) 276 253 1. Norfolk 2. Raleigh 3. Boston 349 480 4. Bangor 5. Philadelphia 282 Norfolk, Raleigh, New York Norfolk, Raleigh, Richmond Boston, Bangor, Philadelphia, Baltimore, New York, Pittsburgh Boston, Bangor, Philadelphia, Pittsburgh Boston, Bangor, Philadelphia, Baltimore, New York, Wilmington Boston, Philadelphia, Baltimore, New York, Wilmington Norfolk, Boston, Philadelphia, Baltimore, New York, Wilmington Boston, Bangor, Pittsburgh, Richmond Raleigh, Pittsburgh, Richmond Philadelphia, Baltimore, New York, Wilmington 6. Baltimore 385 7. New York 268 8. Pittsburgh 9. Richmond 10. Wilmington 323 358 268