2006年美国数学建模竞赛赛题（English）
2006 年美国大学生数学建模竞赛 MCM、ICM 试题
高低压正常范围2006 MCM A: Positioning and Moving Sprinkler Systems for Irrigation
There are a wide variety of techniques available for irrigating a field. The technologies range from advanced drip systems to periodic flooding. One of the sys tems that is ud on smaller ranches is the u of “hand move” irrigation systems. Lightweight aluminum pipes with sprinkler heads are put in place across fields, and they are moved by hand at periodic intervals to insure that the whole field receives an adequate amount of water. This type of irrigation system is cheaper and easier to maintain than other systems. It is also flexible, allowing for u on a wide variety of fields and crops. The disadvantage is that it requires a great deal of time and effort to move and t up the equipment at regular intervals. .
Given that this type of irrigation system is to be ud, how can it be configured to minimize the amount of time required to irrigate a field that is 80 meters by 30 meters? For this task y
ou are asked to find an algorithm to determine how to irrigate the rectangular field that minimizes the amount of time required by a rancher to maintain the irrigation system. One pipe t is ud in the field. You should determine the number of sprinklers and the spacing between sprinklers, and you should find a schedule to move the pipes, including where to move them.
A pipe t consists of a number of pipes that can be connected together in a straight line. Each pipe has a 10 cm inner diameter with rotating spray nozzles that have a 0.6 cm inner diameter. When put together the resulting pipe is 20 meters long. At the water source, the pressure is 420 Kilo- Pascal’s and has a flow rate of 150 liters per minute. No part of the field should receive more than 0.75 cm per hour of water, and each part of the field should receive at least 2 centimeters of water every 4 days. The total amount of water should be applied as uniformly as possible. .
安乐妙宝
2006 MCM B: Wheel Chair Access at Airports
疯流女管家
诸葛亮《诫子书》One of the frustrations with air travel is the need to fly through multiple airports, and each
stop generally requires each traveler to change to a different airplane. This can be especially difficult for people who are not able to easily walk to a
群收款different flight\'s waiting area. One of the ways that an airline can make the transition easier is to provide a wheel chair and an escort to tho people who ask for help. It is generally known well in advance which pasngers require help, but it is not uncommon to receive notice when a pasnger first registers at the airport. In rare instances an airline may not receive notice from a pasnger until just prior to landing.越发的近义词是什么
菩提书院Airlines are under constant pressure to keep their costs down. Wheel chairs wear out and are expensive and require maintenance. There is also a cost for making the escorts available. Moreover, wheel chairs and their escorts must be constantly moved around the airport so that they are available to people when their flight lands. In some large airports the time required to move across the airport is nontrivial. The wheel chairs must be stored somewhere, but space is expensive and verely limited in an airport terminal. Also, wheel chairs left in high traffic areas reprent a liability risk as people try to move a
round them. Finally, one of the biggest costs is the cost of holding a plane if someone must wait for an escort and becomes late for their flight. The latter cost is especially troubling becau it can affect the airline\'s average flight delay which can lead to fewer ticket sales as potential customers may choo to avoid an airline. .
Epsilon Airlines has decided to ask a third party to help them obtain a detailed analysis of the issues and costs of keeping and maintaining wheel chairs and escorts available for pasngers. The airline needs to find a way to schedule the movement of wheel chairs throughout each day in a cost effective way. They also need to find and define the costs for budget planning in both the short and long term.
Epsilon Airlines has asked your consultant group to put together a bid to help them solve their problem. Your bid should include an overview and analysis of the situation to help them decide if you fully understand their problem. They require a detailed description of an algorithm that you would like to implement which can determine where the escorts and wheel chairs should be and how they should move throughout each day. The goal is to ke
ep the total costs as low as possible. Your bid is one of many that the airline will consider. You must make a strong ca as to why your solution is the best and show that it will be able to handle a wide range of airports under a variety of circumstances. . Your bid should also include examples of how the algorithm would work for a large (at least 4 concours), a medium (at least two concours), and a small airport (one concour) under high and low traffic loads. You should determine all potential costs and balance their respective weights. Finally, as populations begin to include a higher percentage of older people who have more time to travel but may require more aid, your report should include projections of
potential costs and needs in the future with recommendations to meet future needs.
2006 ICM: Trade-offs in the fight against
HIV/AIDS
安息的意思As the HIV/AIDS pandemic enters its 25th year, both the number of infections and numbe
r of deaths due to the dia continue to ri. Despite an enormous amount of effort, our global society remains uncertain on how to most effectively allocate resources to fight this epidemic. .
You are a team of analysts advising the United Nations (UN) on how to manage the available resources for addressing HIV/AIDS. Your job is to model veral scenarios of interest and to u your models to recommend the allocation of financial resources. The narrative below provides some background information, and outlines specific tasks.
Task #1: For each of the continents (Africa, Asia, Europe, North America, Australia, and South America), choo the country you believe to be most critical in terms of HIV/AIDS. Build a model to approximate the expected rate of change in the number of HIV/AIDS infections for the countries from 2006 to 2050, in the abnce of any additional interventions. Fully explain your model and the assumptions that underlie your model. In addition, explain how you lected the countries to model.
