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10. It is planned to use drones for enemy areas that need to be photographed from above during the war. The coordinates of ten
10. It is planned to use drones for enemy areas that need to be photographed from above during the war. The coordinates of ten enemy points and the number of places to be photographed are given in the table below (coordinates are given in two of kilometers). Road transport vehicles are used to take the drones to the flight points. Drone flights are planned from 5 predetermined points which are located at the points P1 = (58,63), P2 = (72,58), P3 = (60,52), P4 = (48,80) 4 = and P5 (50,35) (coordinates are given in two of kilometers). Drones travel the Euclidean distance in their flight between two points. However, due to the energy consumption of drones, flight times are limited. Drones stay in the air for a maximum of 120 minutes and fly at a speed of 130 km per hour. The drone has to take pictures and return to the point where it originated. Photo taking time is ignored. Enemy Points Coordinate(x,y) # of places to scan (0,5) 120 (10,20) 200 (15,8) 150 (25, 30) 100 (20, 10) 250 (35, 20) 145 (12, 15) 135 (28,26) 170 (13,23) (8,0) 300 240 a) Determine the minimum number of drones, and their locations to cover all the enemy disricts. Formulate an appropriate mathematical model and solve by Gams. b) If army has only 3 drones, find the optimal locations for a maximal coverage. Formulate an appropriate mathematical model and solve by Gams.
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