2002美国数学建模数学竞赛试题及翻译.doc

2002 MCM A: Wind and Waterspray An ornamental fountain（喷泉） in a large open plaza（广场） surrounded by buildings squirts（喷水池） water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area.Your task is to devise an algorithm（算法） which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.风和喷水池在一个露天广场里装饰喷泉把水喷到控制，当有风吹过时，水滴飘向行人。喷泉射出的水流是由一个与风速计（用于测量风的速度和方向）项链的机械装置控制的，风速计安装在一幢邻近楼房顶上。这个控制的实际作用是要为行人在赏心悦目的景象和淋水浸湿之间提供可以接受的平衡点：风刮的越猛，水量和喷射的高度就越低，从而较少的水花落在水池范围以外。你的任务是设计一个算法，随着风力条件的变化，运用风速计给出的数据来调整由喷泉射出的水流。 2002 MCM B: Airline Overbooking Youre all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat. Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations. Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive. Consider the overbooking issue in light of the current situation: Less flights by airlines from point A to point B heightened security at and around airports Passengers fear Loss of billions of dollars in revenue by airlines to date .Build a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the companys revenue is maximized. Insure that your model reflects the issues above, and consider alternatives for handling “bumped” passengers. Additionally, write a short memorandum to the airlines CEO summarizing your findings and analysis.航空公司超员订票你准备好行装打算去纽约访问的一位挚友。在检票处登记之后，航空公司职员告诉说，你的航班已经超员订票了。乘客们应当马上登记以便确定他们是否还有一个座位。航空公司一向清楚，只有部分比例的预订某个航班的乘客能乘坐该航班。因而，大多数航空公司超员订票，也就是说，他们办理超过飞机容量的订票手续。而有时，需要乘坐一个航班的乘客是飞机容纳不下的，导致一位或多位乘客被挤出而不能乘坐他们预订的航班。航空公司安排被挤出的乘客的方式很多。有些的不到任何补偿，有些改定到其他航线的稍后航班，而有些给予某种现金或机票折扣。根据当前情况，考虑超员订票问题： 1、航空公司安排较少的从A地到B地的航班 2、 机场及其外围加强安全性 3、乘客的恐惧 4、航空公司的收