A Lebanese firm wants to locate a distribution center that will serve six of its major...

   

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A Lebanese firm wants to locate a distribution center that will serve six of its major cities: Tripoli, Zahle, Beirut, Baabda, Saida and Nabatiye. Few criteria have been chosen te optimize the location of the center including: The locations (x, y) of the cities as well as the approximate number of inhabitants. For further details, check the table below: LEBANON Political Map City Number of Coordinate Coordinate Inhabitants UBAN NORO Tripoll Beirut Baabda Nabatiye Zahle Saida 265 495 1,200,000 20,000 Chetk 255 280 525 Sia Amioun 780 Batroun 100,000 60,000 60,000 200,000 Douma MediterraneaN 450 520 680 190 Sea 205 Tripoli MONT-LIBAN 420 BÉIRUTSUorld.c Com Baibda Zahe Also given, the weekly delivery cost C for city i that depends on the number of inhabitants N, per city and the distance D; from the distribution center. For the sake of simplicity, we will assume that this distance is the straight line distance. Thus, the weekly cost is given by the relationship C = D;N for i = 1,2, ... 6. Answer the following questions: 1. Find the location of the distribution center that SYRIAN ARAB REPUBLIC Sidon anONr a NABATIYE LEGEND ISRAEL Capyrhe 201-12 www.alran OherCan minimizes the total weekly cost to service all six cities. For this purpose you are required to implement a MATLAB program that is capable to compute the coordinates of this location. 2. Plot the location of the center on top of the image Lebanon-map.jpg. For this purpose, you should do a research on image processing in MATLAB. A Lebanese firm wants to locate a distribution center that will serve six of its major cities: Tripoli, Zahle, Beirut, Baabda, Saida and Nabatiye. Few criteria have been chosen te optimize the location of the center including: The locations (x, y) of the cities as well as the approximate number of inhabitants. For further details, check the table below: LEBANON Political Map City Number of Coordinate Coordinate Inhabitants UBAN NORO Tripoll Beirut Baabda Nabatiye Zahle Saida 265 495 1,200,000 20,000 Chetk 255 280 525 Sia Amioun 780 Batroun 100,000 60,000 60,000 200,000 Douma MediterraneaN 450 520 680 190 Sea 205 Tripoli MONT-LIBAN 420 BÉIRUTSUorld.c Com Baibda Zahe Also given, the weekly delivery cost C for city i that depends on the number of inhabitants N, per city and the distance D; from the distribution center. For the sake of simplicity, we will assume that this distance is the straight line distance. Thus, the weekly cost is given by the relationship C = D;N for i = 1,2, ... 6. Answer the following questions: 1. Find the location of the distribution center that SYRIAN ARAB REPUBLIC Sidon anONr a NABATIYE LEGEND ISRAEL Capyrhe 201-12 www.alran OherCan minimizes the total weekly cost to service all six cities. For this purpose you are required to implement a MATLAB program that is capable to compute the coordinates of this location. 2. Plot the location of the center on top of the image Lebanon-map.jpg. For this purpose, you should do a research on image processing in MATLAB.

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