(just formulate it). In hand writiting 11.2 North Penberthy Housing Association
ID: 390121 • Letter: #
Question
(just formulate it). In hand writiting
11.2 North Penberthy Housing Association is planning a number of blocks of flats. Five types of block have been designed, containing flats of four categories (1 - senior citizens, 2 - single person, 3 - small family and 4-large family). The number of flats in each block, and other relevant information, is as follows: Type of Number of flats Number Plan Cost per block in category of storeys area block 1 2 3 4 (Smillion) 1 2 4 0 3 0 3 6 0 6 2 22 4 2 0 60 88 0 0 10 5 3 5 2.08 3.2 8 3.0 6 4.8 4 4.8 The association wants to build a total of 500 flats with at least 40 in category 1 and 125 in each of the other categories. In the past, high-rise flats have proved unpopular and the association wants to limit the number of storeys in the development - with the average number of storeys at most five, and at least half the flats in blocks of three or fewer storeys. An area of 300 units has been set aside for the development and any spare land will be used as a park. Formulate this problem as a linear programme.Explanation / Answer
LP formulation is following:
Let A,B,C,D,E be the number of blocks to to build of the five types respectively
Min 2.08A+3.2B+3C+4.8D+4.8E (total Cost)
s.t.
(1+2+4)A+(3+6)B+(2+2+2+4)C+(6+8)D+(10+5)E = 500 (total of 500 flats)
A+2C >= 40 (at least 40 flats in categroy 1)
2A+3B+2C+6D >= 125 (125 flats in category 2)
4A+6B+2C+10E >= 125 (125 flats in category 3)
4C+8D+5E >= 125 (125 flats in category 4)
3A+6B+2C+8D+3E <= 5(A+B+C+D+E) (average number of stories at most 5)
(1+2+4)A+(2+2+2+4)C+(10+5)E >= 250 (at least half the flats in blocks of 3 or fewer stories)
5A+5B+8C+6D+4E <= 300 (area of 300 units set aside for the development)
A,B,C,D,E >= 0
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