Airplane maintenance Boeing needs to build 5 maintenance centers for the Euro-Asian area. The construction cost for each center is 300 million euros in the European area (between 20 W and 40 E) and 150 million euros in the Asian area (between 40 E and 160 E), as shown below. Each center can service up to 60 airplanes each year. The centers should service the airports with the highest number of Boeing customers, as detailed in the table below (airport name, geographical coordinates, expected number of airplanes/year needing maintenance). Airport Coordinates N. of planes London 51 N 0 W 30 Frankfurt 51 N 8 E 35 Lisboa 38 N 9 W 12 Z¨urich 47 N 8 E 18 Roma 41 N 12 E 13 Abu Dhabi 24 N 54 E 8 Moskva 55 N 37 E 15 Vladivostok 43 N 132 E 7 Sydney 33 S 151 E 32 Tokyo 35 N 139 E 40 Johannesburg 26 S 28 E 11 New Dehli 28 N 77 E 20 The total cost is given by the construction cost plus the expected servicing cost, which depends linearly on the distance an airplane needs to travel to reach the maintenance center (weighted by 50 euro/km). We assume earth is a perfect sphere, so that the shortest distance between two points with geographical coordinates (x1, y1) and (x2, y2) is given by: d(x1, y1, x2, y2) = 2r asin (sqrt [sin^2((x1 - x2)/2) + cos x1 * cos x2 * sin^2((y1 - y2)/2) ]), where r, the earth radius, is 6371km. Formulate a (nonlinear) mathematical program to minimize the operation costs.