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Unformatted text preview: Sabanci university Faculty of Engineering and Natural Sciences Industrial Engineering Final exam MS 301 January 19th 2011, FENS G077,G025 16.00-18.00. Remark: keep your answers as short as possible but of course complete. Also read very carefully the questions. The total number of points of this exam is 100. At the beginning of each part of the exercise the total number of points are listed. Please write your student number at each page and write clearly. To avoid too many disturbances for the other students you are only allowed to ask questions about the exam in the first hour. The makeup will be held on January 22th , FENS G032, FENS G035 and L035, 11:00-13:00. Exercise 1. (30 points) The city of Orhanlı is faced with a abundance of substandard houses which are not occupied and a severe budget shortage. Seeking a long term solution, the city council votes to improve the tax base by condemning an inner-city housing area and replacing it with a modern development. The project involves two phases: (1) demolishing the substandard empty houses to provide land for the new development and (2) building the new development. The following is a summary of the situation 1. As many as 300 substandard empty houses can be demolished. Each house occupies a . 25 acre lot. The cost of demolishing a condenmed house is 2000 TL 2. Lot sizes for new single-, double-, triple- and quadruble family home units are . 18 , . 28 , . 4 and . 5 acre, respectively. Streets, open space and utility easements account for 15 percent of the available acreage. 3. Due to the composition of the local population in the Istanbul area and the desire to balance the future population of Orhan over singles and small and large families it is decided by the council that in the new development the triple and quadruble units account for at least 25 percent of the total. Single units must be at least 20 percent of all units and double units at least 10 percent. 4. The tax levied per unit for an occupied single ,double, triple and quadruble units is 1000 TL, 1900 TL, 2700 TL and 3400 TL 5. The construction costs per unit paid by the city of Orghanlı for single-,double-, triple- and quadruble family homes is 50 . 000 TL, 70 . 000 TL, 130 . 000 TL and 160 . 000 TL.,respectively. The city of Orhanlı can finance everything through ther local Akbank to a maximum of 15 milliıon TL. It is expected by the council that the loan can be easily covered by the rental 1 income from the new houses and due to the shortage of good housing that all the new build houses will not stay empty. Since the city of Orhanli is interested in maximizing their tax revenue formulate the corre- sponding optimization problem. Define clearly the used decision variables....
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