A courier company wants to determine the optimal location of collection points from which parcels will be collected by their drivers and delivered to their customers. The map above shows the locations of their frequent customers (blue dots) and the locations of potential collection points (red squares). The units of the axis for the map are in kilometers. The complete data set is provided below. Formulate the problem as a facility location problem by taking the straight line distance from a customer to a potential collection point as a proxy for the traveling distance. Make use of GMPL to determine which collection points should be operational, by considering a traveling cost of R8.50/km. The frequency of delivery to each customer is assumed to be the same for all customers. Provide the Excel file with your GMPL code as your answer sheet and clearly indicate the coordinates of the collection points which form part of the optimal solution

customer	x-location	y-location
1	2,64168218	2,816248054
2	6,187017426	4,954069643
3	5,33005768	9,224219489
4	2,315744499	4,201178014
5	3,611560411	9,531846065
6	6,267281106	6,729026154
7	5,873287149	4,248481704
8	4,505447554	4,163029878
9	9,175389874	1,377605518
10	0,468764306	8,850672933
11	3,492233039	4,946440016
12	5,223548082	3,144627216
13	0,111087374	1,058381909
14	5,561693167	6,3615833
15	7,00552385	3,0262154
16	4,851222266	3,47972045
17	8,991058077	2,148808252
18	6,954252754	4,637287515
19	5,481734672	5,696584979
20	8,522293771	9,494308298
21	3,655507065	8,664510025
22	9,983520005	5,519272439
23	9,841303751	0,859401227
24	0,535599841	4,265877255
25	6,942350536	5,880916776
26	7,452925199	4,698019349
27	0,70741905	3,557847835
28	5,022125919	7,63145848
29	2,662129582	2,406689657
30	3,422040468	0,346079897
31	2,510147404	3,669850764
32	2,855311747	5,44389172
33	7,824640645	3,500778222
34	3,246253853	2,999664296
35	3,83373516	4,853358562
36	4,818872646	0,08148442
37	1,116061892	5,644093142
38	9,864803003	6,693319498
39	4,021423994	4,742881558
40	1,017181921	2,20557268
41	7,624744407	2,360606708
42	6,339915159	1,340372936
43	6,026795251	6,393627735
44	6,543168432	3,765984069
45	9,818414869	1,286049989
46	4,646137883	6,368907743
47	5,513473922	0,976897488
48	3,388470107	2,262337107
49	4,770348216	2,489089633
50	0,710165716	5,600756859

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12 10 . 00 Distance (km) 6 2 2 0 0 2 6 10 12 Distance (km) collection point x-location y-location capacity setup cost 12,569841609 4,010010071 22 320000 2 3,482284005 7,805352947 36 235000 37,262062441 2,67751091 14 90000 4 8,324622 6,481460005 19 175000 5 5,328226569 6,004638813 29 250000 6 4,244490307 1,87902345 31 100000 12 10 . 00 Distance (km) 6 2 2 0 0 2 6 10 12 Distance (km) collection point x-location y-location capacity setup cost 12,569841609 4,010010071 22 320000 2 3,482284005 7,805352947 36 235000 37,262062441 2,67751091 14 90000 4 8,324622 6,481460005 19 175000 5 5,328226569 6,004638813 29 250000 6 4,244490307 1,87902345 31 100000