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# American Parcel Service American Parcel Service (APS) has deternimined that it needs to add several new package distribution hubs to service twelve...

Please provide me with an algebraic equation for #1 on the attached pdf.
Page 1 of 2 American Parcel Service American Parcel Service (APS) has deternimined that it needs to add several new package distribution hubs to service twelve cities east of the Mississippi River. The company wants to construct the minimum set of new hubs for the following 12 cities so that there is a hub within 300 miles of every city (i.e., every city is covered by a hub). City Cities Within 300 Miles 1. Atlanta Atlanta, Charlotte, Nashville 2. Boston Boston, New York 3. Charlotte Atlanta, Charlotte, Richmond 4. Cincinnati Cincinnati, Detroit, Nashville, Pittsburgh 5. Detroit Cincinnati, Detroit, Indianapolis, Milwaukee, Pittsburgh 6. Indianapolis Cincinnati, Detroit, Indianapolis, Milwaukee, Nashville, St. Louis 7. Milwaukee Detroit, Indianapolis, Milwaukee 8. Nashville Atlanta, Cincinnati, Indianapolis, Nashville, St. Louis 9. New York Boston, New York, Richmond 10. Pittsburgh Cincinnati, Detroit, Pittsburgh, Richmond 11. Richmond Charlotte, New York, Pittsburgh, Richmond 12. St. Louis Indianapolis, Nashville, St. Louis GOAL: minimize the number of new hubs to be added to APS. DECISION: identify those cities that will have the new hubs. REQUIREMENT: each of the 12 cities must be within 300 miles of a hub. ASSIGNMENT: 1. Formulate the algebraic model for this situation 2. Provide a spreadsheet model and a Solver solution that meets the requirement that each city is within 300 miles of its hub. Consider that these 12 cities are spread over five regional areas as follows: Region Cities Within a Region 1 Boston, New York, Pittsburgh 2 Atlanta, Nashville 3 Cincinnati, Detroit, Milwaukee 4 Indianapolis, St. Louis 5 Charlotte, Richmond ASSIGNMENT: 3. Provide a Solver solution that meets the added requirement that there must be at least one hub in each region. 4. Provide a solver solution that meets the added requirements: a. Boston and New York cannot both have a hub b. There must be a hub in either Nashville or Richmond
Page 2 of 2 Start-up costs have been estimated for locating a hub in each city. They are as follows: City S t a r t - u p C o s t Atlanta \$450,000 Boston \$275,000 Charlotte \$175,000 Cincinnati \$150,000 Detroit \$160,000 Indianapolis \$310,000 Milwaukee \$290,000 Nashville \$200,000 New York \$435,000 Pittsburgh \$100,000 Richmond \$90,000 St. Louis \$115,000 ASSIGNMENT: 5. Provide a Solver solution that will minimize the overall start-up cost while meeting all of the previous requirements. 6. Comment on other factors not mentioned in this problem and how they might affect the outcome, i.e., looking beyond the stated requirements.

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