The governership of zmir has tasked you with the duty to determine ambulance stations for Bornova. Bornova is made up of 20 neighbourhoods. Each neighbourhood and its population is given in Table 1. For ease of reference, instead of the names of the neighbourhoods, they are numbered from 1 to 20. You have to choose enough number of ambulance station locations among 10 possible locations. Lets number these possible locations j=1 to 10. Each neighbourhood must be assigned to exactly one active (chosen) ambulance station. The distances between these neighbourhoods and the possible locations are given in Table 2. Opening an ambulance station has a cost. If you build an ambulance station to possible location j, it will cost f(lj) =20,000+0.5x, where x is the total population of neighbourhoods served by this station. This means the cost of opening one ambulance station at any location, should you decide to do it, has 20,000 TL fixed cost and variable cost in proportion to the number of people that it will serve. The total budget allocated for all ambulance stations in Bornova is 300,000TL. There are 2 major hospitals in Bornova: Ege University School of Medicine Hospital and Trkan zilhan Trauma Hospital. There will definitely be one ambulance station at each of these hospitals. Both hospitals have 2 possible locations for an ambulance station within their walls. Lets call the possible locations at Ege University School of Medicine Hospital, locations 1 and 2; and the locations within Trkan zilhan Trauma Hospital, locations 3 and 4. Due to land survey/political reasons, either locations 5 and 6 or locations 9 and 10 must be selected as ambulance stations. You have to determine the best locations for ambulance stations and the assignment of neighbourhoods to stations. Your objective is to minimize the distance travelled to the neighbourhood farthest from its assigned ambulance station.

Write the full mathematical model for this problem (Define your parameters, decision variables and constraints clearly) ,

,

Table 1 Populations of neighbourhoods 1 2 3 4 5 6 7 8 12 14 15 16 17 18 19 20 Neighbourhood 9 10 11 13 Population 31075 31060 27260 24876 22236 20674 20372 19263 19026 14746 14512 13996 12562 12311 10509 10453 10286 8649 8264 8141 Table 2 Distances between potential locations and neighborhoods 1 2. 3 5 6 7 Neighbourhood 8 | 9 | 10 11 90 38 81 84 12 13 14 15 16 17 18 19 20 1 72 39 90 36 68 88 55 30 47 79 78 43 58 52 79 97 21 45 32 83 49 94 64 90 90 51 36 23 57 40 64 35 87 77 23 71 2 3 64 76 25 52 70 31 73 63 64 27 88 42 89 24 79 93 46 52 40 40 4 37 49 36 35 98 95 62 38 77 73 88 73 23 29 34 45 33 66 36 79 5 79 45 69 97 60 47 51 71 22 33 21 69 59 60 60 32 29 62 41 22 location (1) Potential 6 50 83 102 58 62 99 93 21 37 73 47 74 49 48 44 61 24 53 90 31 7 105 44 21 29 23 52 96 64 44 74 54 58 45 38 95 53 84 63 59 82 8 54 98 75 32 38 92 59 98 53 42 34 41 67 43 52 68 77 32 56 88 9 100 93 46 52 80 39 25 91 39 56 83 41 46 55 23 61 55 74 33 61 10 23 93 59 79 60 24 90 30 87 66 26 85 43 51 87 47 68 72 79 93 Table 1 Populations of neighbourhoods 1 2 3 4 5 6 7 8 12 14 15 16 17 18 19 20 Neighbourhood 9 10 11 13 Population 31075 31060 27260 24876 22236 20674 20372 19263 19026 14746 14512 13996 12562 12311 10509 10453 10286 8649 8264 8141 Table 2 Distances between potential locations and neighborhoods 1 2. 3 5 6 7 Neighbourhood 8 | 9 | 10 11 90 38 81 84 12 13 14 15 16 17 18 19 20 1 72 39 90 36 68 88 55 30 47 79 78 43 58 52 79 97 21 45 32 83 49 94 64 90 90 51 36 23 57 40 64 35 87 77 23 71 2 3 64 76 25 52 70 31 73 63 64 27 88 42 89 24 79 93 46 52 40 40 4 37 49 36 35 98 95 62 38 77 73 88 73 23 29 34 45 33 66 36 79 5 79 45 69 97 60 47 51 71 22 33 21 69 59 60 60 32 29 62 41 22 location (1) Potential 6 50 83 102 58 62 99 93 21 37 73 47 74 49 48 44 61 24 53 90 31 7 105 44 21 29 23 52 96 64 44 74 54 58 45 38 95 53 84 63 59 82 8 54 98 75 32 38 92 59 98 53 42 34 41 67 43 52 68 77 32 56 88 9 100 93 46 52 80 39 25 91 39 56 83 41 46 55 23 61 55 74 33 61 10 23 93 59 79 60 24 90 30 87 66 26 85 43 51 87 47 68 72 79 93