A math problem
5.12 Wenchuan earthquake zone so that the earthquake ground transportation and communication systems severely paralyzed. Command to send more emergency relief support teams, each assigned to the regional implementation of the search task to determine the need for rescue personnel the exact location. In other occasions, often similar to the search mission. In such an emergency need to be resolved is one of the important issues: the development of the search team road line, scheduled for the region’s fast full search. Typically, each of the search personnel with a GPS positioning device, walkie-talkie, as well as daily necessities such as food and equipment. In the ranks of a certain number of satellite telephone. GPS allows officers to search their own position. Walkie-talkie to communicate with each other. Satellite phones to be used to search the headquarters of the report the situation.
The following is a simplified search problems. A flat rectangular target area, the size of 11,200 m × 7200 meters, the need for the whole territory of the search. Assumptions: the starting point in the central region; search after the completion of the necessary build-up, the assembly point (end point) in the short to the left side of the mid-point; everyone when the search detection can be a radius of 20 meters, the search for the average road speed 0.6 m / s ; Not just search the road, an average speed of 1.2 m / sec. Everyone with a GPS positioning device, walkie-talkies, walkie-talkie communication with a radius of 1,000 meters. Search teams a set number of man-made, a team leader, also head of the satellite phone. Everyone to search for goals, the need to use walkie-talkie in a timely manner to the head of the report, the head of the headquarters by satellite phone to report the latest results of the search.
There are problems to be solved as follows:
1. The assumption that there is a 20-member team of the search team, have a satellite phone. Please design a time-consuming do you think the shortest way to search. In accordance with the way you search the entire region is the number? Can search within 48 hours to complete the task? If not completed, the number of personnel needed to complete the task.
2. In order to speed up the pace of the search team of 50 people, with 3 satellite phones, divided into 3 groups to carry out the search. Each search will be an independent report to the command. Please do you think the design of a time-consuming search of the shortest way. In accordance with your search, search the entire region is the number?
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