130 120 09 2 X ZONE 2 110 Hospital X Coordinate Y Coordinate Shipments/week Recall the class example where we wanted to locate a 20 20 5 2 30 80 25 3 60 30 20 4 100 100 35 70 110 15 5 central lab where five local hospitals could all Y s 100 send their blood tests to that one location, at minimum total weekly travel distance possible. 2 The coordinate of each hospital and number of test shipments per week that would be sent to the lab were given as: 100 4 90 X + 2Y 2260 80 70 Coordinate + Y + 2XS 180 60 ZONE 1 50 40 30 20 1 X 570 10 0 0 10 20 30 40 70 80 90 100 110 50 60 X-Coordinate 3 Suppose there are local zoning boundaries as shown in the map. The lab should either be located in Zone 1 (i.e., its coordinates should satisfy the three constraints that define Zone boundaries) or in Zone 2 (i.e., its coordinates should satisfy the two constraints that define Zone 2 boundaries). The red area between the two zones is designated as national conservation area in which we cannot obtain building permits. The optimal coordinates (71.3, 88.1) that we got in class clearly fall in the restricted area and therefore are not acceptable. a) Write an algebraic formulation for this problem. (10 pts) (Hints: Binary Variables, Big-M constraints). b) Solve your formulation in Excel or Python (your choice). Report the solution and attach your file. (5 pts) c) Looking at the zoning map above, briefly comment on whether the feasible region, i.e., the allowed area for lab coordinates, is convex or nonconvex. (5 pts) 130 120 09 2 X ZONE 2 110 Hospital X Coordinate Y Coordinate Shipments/week Recall the class example where we wanted to locate a 20 20 5 2 30 80 25 3 60 30 20 4 100 100 35 70 110 15 5 central lab where five local hospitals could all Y s 100 send their blood tests to that one location, at minimum total weekly travel distance possible. 2 The coordinate of each hospital and number of test shipments per week that would be sent to the lab were given as: 100 4 90 X + 2Y 2260 80 70 Coordinate + Y + 2XS 180 60 ZONE 1 50 40 30 20 1 X 570 10 0 0 10 20 30 40 70 80 90 100 110 50 60 X-Coordinate 3 Suppose there are local zoning boundaries as shown in the map. The lab should either be located in Zone 1 (i.e., its coordinates should satisfy the three constraints that define Zone boundaries) or in Zone 2 (i.e., its coordinates should satisfy the two constraints that define Zone 2 boundaries). The red area between the two zones is designated as national conservation area in which we cannot obtain building permits. The optimal coordinates (71.3, 88.1) that we got in class clearly fall in the restricted area and therefore are not acceptable. a) Write an algebraic formulation for this problem. (10 pts) (Hints: Binary Variables, Big-M constraints). b) Solve your formulation in Excel or Python (your choice). Report the solution and attach your file. (5 pts) c) Looking at the zoning map above, briefly comment on whether the feasible region, i.e., the allowed area for lab coordinates, is convex or nonconvex. (5 pts)