Innis Construction Company specializes in building moderately priced homes in Cincinnati, Ohio. Tom Innis has identified eight potential locations to construct new single-family dwellings, but he cannot put up homes on all of the sites because he has only

$300,000 to invest in all projects. The following table shows the cost of constructing homes in each area and the expected profit to be made from the sale of each home. Note that the home-building costs differ considerably due to lot costs, site preparation, and differences in the models to be built. Note also that a fraction of a home cannot be built.

(a) Formulate Innis’s problem using 0–1 integer programming.

(b) Solve with QM for Windows or Excel.

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COST OF BUILDING EXPECTED LOCATION AT THIS SITE ($) PROFIT ($) Clifton 60,000 5,000 Mt. Auburn 50,000 6,000 Mt. Adams 82,000 10,000 Amberly 103,000 12,000 Norwood 50,000 8,000 Covington 41,000 3,000 Roselawn 80,000 9,000 Eden Park 69,000 10,000