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apdCD AaBbCcbde AaBb Heading 1 Heading 2 AaBb CcDdEe Normal No Spacing Subtitle The Millennium Development Corporation has just received a small hotel for conversion to condominium apartments. The building, in a popular area of Washington, D.C., near the U.S. State Department will be highly marketable, and each condominium sale is expected to yield a good profit. The conversion process, however, includes several options. Basically, four types of condominiums can be designed out of the former hotel rooms. They are deluxe one bedroom apartments, regular one-bedroom apartments, deluxe studios, and efficiency apartments. Each will yield a different profit, but each type also requires a different level of investment in carpeting, painting, appliances, and carpentry work. Bank loans dictate a limited budget that may be allocated to each of these needs. Profit and cost data, and cost of conversion requirements for each apartment are shown in the accompanying table. Efficiency Deluxe one- Regular bedroom (S) one- bedroom (S) 1,100 1,000 studio ((S) Total budgeted (5) 600 500 35,000 400 300 700 2,000 600 1,600 1,200 900 28,000 44,600 New carpeting Painting New appliances Carpentry work Profit per unit 1,000 400 900 200 18,800 10,000 7,000 6,000 4,000 Thus, the cost of carpeting a deluxe one-bedroom unit will be $1,100, the cost of carpeting a regular one-bedroom unit will be $1,000, and so on. A total of $35.000 is budgeted for all new carpeting in the building. Zoning regulations dictate that the building contain no more than 50 condominiums when the conversion is completed - and no lass than 25 units. The development company also decides that to have a good blend of owners, at least 40% but no more than 70% of the units should be one bedroom apartments. Not all money budgeted in each category need to be spent, although profit is not affected by cost savings. But since the money represents a bank loan, under no circumstances, may it be exceeded or even shifted from one area, such as carpeting, to another, such as painting. The decision problem facing Millennium Development Corporation was formulated and solved using Linear Programming. The decision variables used in the formulation are: DB-number of deluxe one-bedroom units to convert RB-number of regular one-bedroom units to convert DS-number of deluxe studio units to convert E-number of efficiency units to convert DTU abe 2 x A A Max 10000DB + 7000RB + 6000DS + 4000E s.t. Carpet) 1100DB + 1000RB + 600DS + 500E =25 1bedmin) 0.6DB + 0.6RB - 0.4DS - 0.4E > 0 1 bedmax) 0.3DB+ 0.3RB - 0.7DS - 0.7E =25 1bedmin) 0.6DB + 0.6RB - 0.4DS - 0.4E > 0 1 bedmax) 0.3DB+ 0.3RB - 0.7DS - 0.7E