DUE: MONDAY, DECEMBER 8, 2008
Acc. Math I Culminating Task:
Surveillance of the Village
Agents Bourne, Bond, and Chan are assigned to surveillance of the town of Deadwood.
Three roads meet in the center of the town. One road runs directly east-west, and one runs only directly south. The third road starts in the center of town and runs approximately northeast. Bond noticed he could reach the third road by traveling 1 mile east and 2 miles north of the center of the village.
The three agents want to place themselves so they are at least 2 miles outside of town. To ensure adequate radio communication, they must be less than 5 miles apart.
1. Where should they place themselves? Verify your answer mathematically.
2. Are there multiple options for their placements? Which option would you recommend and why?
After a day of surveillance, Bourne decides they need to make sure that all roads leaving town are under surveillance. The agents are concerned about being seen from the road or town but they need to maintain radio contact at all times. Chan drew up the following list of requirements for their placements around the village:
· Each agent should be at least 2 miles from town.
· Each agent should be a least 1⁄2 mile from all roads.
· Each road should be covered by at least one agent that is within 1.5 miles of that road, and an agent can cover more than one road.
· Each pair of agents should be no more than 5 miles apart.
3. Where should the agents place themselves in order to meet all of the above requirements?
4. Could there be more than one arrangement of the agents? Verify all answers mathematically.
Bourne wishes to add a repeater, an electronic device that receives and rebroadcasts radio signals, to improve the radio communication between the agents. He wishes to place the repeater in a location close to all three agents.
5. Where should he place it? Why? Justify your answer mathematically.
Chan is concerned there is not enough coverage of the village and asks for one more agent.
6. Leaving the Bourne, Bond, and Chan in place, where should the 4th agent be placed? Justify your answer.
7. Should he change the placement of all agents to get better coverage of the village? Justify your answer.
8. What are the advantages and disadvantages of having three agents? Include a defense of your position.
9. What are the advantages and disadvantages of having four agents? Include a defense of your position.
NOTES FOR PROJECT:
1. You may work with a partner, but each person must submit a completed project for grading. Please let me know ahead of time if you are working with a partner.
2. The concepts used in this project will be taught throughout the month of November, so you may not be able to complete parts of the project until later in the month. Read over the complete project, though, so that you can get a basic idea of what is being asked of you.
3. I will check your progress periodically, beginning during the week of November 10th, so do not wait until the last minute to start this project.
4. Even though it is not explicitly stated, please note that you will need to make several drawings in order to show your solutions.
5. This project is a modified and simplified version of a project that military strategist might work on.