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A real estate company is considering several different hotel projects. They need to build at least 2 hotels, and there are 5 locations under consideration. The company must decide which locations to build hotels on and the number of rooms to build at each of the chosen locations. There are fixed costs associated with each of the locations that will only be incurred if a hotel is built on the location. Also associated with each of the locations is the expected annual profit per room. Finally, there is a room limit for each location that cannot be exceeded. Formulate a mathematical program that can be used to determine the number of rooms to build at each of the locations so that difference between the annual profit and the fixed costs is maximized. Location Fixed Cost Annual Profit/Room Max # Rooms 1 $8000 $500 100 2 $3000 $100 300 3 $6500 $350 150 4 $4000 $300 200 5 $7000 $550 50
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