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The Domino Company sells copying machines in six cities: Boston, New York, Philadelphia, Washington D.C., Providence, and Atlantic City. A major factor in making a sale is Domino’s quick service. The annual sales of copiers projected depend on whether a service representative is within 150 miles of a city. The left table below provides the projected annual sales in each city in two conditions: (1) at least one service representative is within 150 miles, and (2) no service representative is within 150 miles. Each copier costs $500 to produce and sells for $1000. The annual cost per service representative is $80,000. Domino must determine in which of its markets to base a service representative. Only Boston, New York, Philadelphia and Washington DC are under consideration as bases for service representatives. The distances (in miles) among the cities are shown in the right table below. Formulate an ILP that will help Domino maximize its annual profit.
Sales (in units) Distance (in miles) Representative within 150 miles? Yes No Boston N.Y. Phil. D.C. Boston 700 500 Boston 0 222 310 441 New York 1000 750 New York 222 0 89 241 Philadelphia 900 700 Philadelphia 310 89 0 146 Washington D.C. 800 450 Washington D.C. 441 241 146 0 Providence 400 200 Providence 47 186 255 376 Atlantic City 450 300 Atlantic City 350 123 82 178

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