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.