UW Mobile wishes to erect a number of cell towers within the UW campus. For each...
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UW Mobile wishes to erect a number of cell towers within the UW campus. For each cell tower, the coverage radius R of the tower (in meters) is directly proportional to the height h of the tower (in meters), according to the formula R = 15h, and the cost c of constructing the tower (in dollars) is directly proportional to the square of the height of the tower (in meters), according to the formula c = 100h². For practical reasons, the minimum possible height of a cell tower is 5 meters. Assume that all towers sprout from ground level. The following list of campus buildings and their (x, y)-coordinates is used for this problem: Building X AL BMH CPH DC DWE E5 y 574 405 Building EV3 569 1066 HH 862 529 NH 742 823 MC 766 471 PAC 901 794 PHY X Y 419 423 Building X 734 RCH 536 310 SCH 468 558 SLC 577 833 STC 408 TC 949 678 610 V1 677 448 526 628 85 Y 535 428 843 662 456 1013 (a) Suppose that UW Mobile has decided to erect two cell towers, and provide network coverage to the following three buildings: MC, HH and NH. Formulate an NLP that determines the minimum-cost configuration of cell towers which provides coverage to these buildings. (b) Now suppose that UW Mobile is building five cell towers, and wishes to provide network coverage to all eighteen buildings listed above. Formulate an NLP that determines the minimum-cost configuration of cell towers which provides coverage to all of the buildings listed above. You may number the buildings 1 to 18 and write (xi, yi) for the coordinates of the i-th building. (c) In continuation of part (b), suppose that the president issues an edict requiring that NH have redundant cell coverage from at least two towers, and that no cell tower within 200 meters of NH may be taller than 10 meters. Modify your NLP from part (b) to accommodate this decree. UW Mobile wishes to erect a number of cell towers within the UW campus. For each cell tower, the coverage radius R of the tower (in meters) is directly proportional to the height h of the tower (in meters), according to the formula R = 15h, and the cost c of constructing the tower (in dollars) is directly proportional to the square of the height of the tower (in meters), according to the formula c = 100h². For practical reasons, the minimum possible height of a cell tower is 5 meters. Assume that all towers sprout from ground level. The following list of campus buildings and their (x, y)-coordinates is used for this problem: Building X AL BMH CPH DC DWE E5 y 574 405 Building EV3 569 1066 HH 862 529 NH 742 823 MC 766 471 PAC 901 794 PHY X Y 419 423 Building X 734 RCH 536 310 SCH 468 558 SLC 577 833 STC 408 TC 949 678 610 V1 677 448 526 628 85 Y 535 428 843 662 456 1013 (a) Suppose that UW Mobile has decided to erect two cell towers, and provide network coverage to the following three buildings: MC, HH and NH. Formulate an NLP that determines the minimum-cost configuration of cell towers which provides coverage to these buildings. (b) Now suppose that UW Mobile is building five cell towers, and wishes to provide network coverage to all eighteen buildings listed above. Formulate an NLP that determines the minimum-cost configuration of cell towers which provides coverage to all of the buildings listed above. You may number the buildings 1 to 18 and write (xi, yi) for the coordinates of the i-th building. (c) In continuation of part (b), suppose that the president issues an edict requiring that NH have redundant cell coverage from at least two towers, and that no cell tower within 200 meters of NH may be taller than 10 meters. Modify your NLP from part (b) to accommodate this decree.
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Organizational Behaviour Concepts Controversies Applications
ISBN: 978-0132310314
6th Canadian Edition
Authors: Nancy Langton, Stephen P. Robbins, Timothy A. Judge, Katherine Breward
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