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Unformatted text preview: AS/2901/1/SC/lp/10-11 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH2901 Operations Research I Assignment 1 * Q1-Q4 require handing in as assignment * * Q5-Q6 will be discussed during R1 class * Due date: 29 September, 2010 (by noon) 1. A 10-acre slum in New York City is to be cleared. The oﬃcials of the city must decide on the redevelopment plan. Two housing plans are to be considered: low-income housing and middle-income housing. The types of housing can be developed at 20 and 15 units per acre, respectively. The unit costs of the low- and middle-income housing are $17,000 and $25,000. The lower and upper limits set by the oﬃcials on the number of low-income housing units are 80 and 120. Similarly, the number of middle-income housing units lie between 45 and 90. The combined maximum housing market potential is estimated to be 190 (which is less than the sum of the individual market limits due to the overlap between the two markets). The total mortgage committed to the renewal plan is not to exceed $2.5 million. Finally, it was suggested by the architectural adviser that the number of low-income housing units be at least 50 units greater than one-half the number of the middle-housing units. (a) Formulate the minimum cost renewal planning problem as a linear program....
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- Fall '11