美国数学建模比赛题目及翻译

1994美国数学建模数学竞赛试题及翻译1994 MCM A: Concrete Slab Floors 住宅的保温HUP公司正在考虑建造从单幢住宅到公寓楼大小不同的住宅。

公司主要关心的是房主定期支付的费用—特别是使暖气和冷气的费用最少。

建房地区位于全年温度变化不大的温带地区。

通过特殊的建筑技术HUP公司能不依靠对流—即不需要依靠开门开窗来帮助调节住宅的温度。

这些住宅都是只有混泥土厚板为仅有基础的单层住宅。

你们被雇佣来分析混泥土地板的温度变化，由此决定地板表面的平均温度能否全年保持在指定的舒适范围内。

如果可能的话，什么样的尺寸和形状能做到这点？第一部分地板温度由表94A-1给G66每天温度的变化范围，试研究混泥土厚板中温度的变化。

假定最高温度在中午到达，最低温度在午夜到达。

试决定能否在只考虑辐射的条件下设计厚板使其表面的平均温度保持在指定的舒适范围内。

一开始，先假定热是通过暴露在外的厚板的周边传入住宅的，而厚板的上、下表面是绝热的。

就这些假设是否恰当、假设的敏感性作出评论。

如果你们不能找到满足表94A-1条件的解，你们能作出满足你们提出的表94A-1的厚板的设计吗？第二部分建筑物温度试分析一开始所做假设的实用性，并将其推广到分析单层住宅温度的变化。

住宅内温度能否保持在舒适范围内。

第三部分建筑费用考虑到建筑的各种限制及费用，试提出一种考虑HUP公司关于降低甚至免去暖气和冷气费用这一目标的设计。

1994 MCM B: Network Design在你们公司里，各部门每天都要分享信息。

这种信息包括前一天的销售统计和当前的生产指南。

尽快公布这些信息是十分重要的。

我们有兴趣的是以最优的方式安排，即使得传输完所有的文件所用的总时间最小。

这个最小总时间称为接通时间。

请为你们的公司考虑以下三种情形：。

历届美国数学建模竞赛赛题, 1985－2006AMCM1985问题-A 动物群体的管理AMCM1985问题-B 战购物资储备的管理AMCM1986问题-A 水道测量数据AMCM1986问题-B 应急设施的位置AMCM1987问题-A 盐的存贮AMCM1987问题-B 停车场AMCM1988问题-A 确定毒品走私船的位置AMCM1988问题-B 两辆铁路平板车的装货问题AMCM1989问题-A 蠓的分类AMCM1989问题-B 飞机排队AMCM1990问题-A 药物在脑内的分布AMCM1990问题-B 扫雪问题AMCM1991问题-A 估计水塔的水流量AMCM1992问题-A 空中交通控制雷达的功率问题AMCM1992问题-B 应急电力修复系统的修复计划AMCM1993问题-A 加速餐厅剩菜堆肥的生成AMCM1993问题-B 倒煤台的操作方案AMCM1994问题-A 住宅的保温AMCM1994问题-B 计算机网络的最短传输时间AMCM1995问题-A 单一螺旋线AMCM1995问题-B A1uacha Balaclava学院AMCM1996问题-A 噪音场中潜艇的探测AMCM1996问题-B 竞赛评判问题AMCM1997问题-A Velociraptor(疾走龙属)问题AMCM1997问题-B为取得富有成果的讨论怎样搭配与会成员AMCM1998问题-A 磁共振成像扫描仪AMCM1998问题-B 成绩给分的通胀AMCM1999问题-A 大碰撞AMCM1999问题-B “非法”聚会AMCM1999问题- C 大地污染AMCM2000问题-A空间交通管制AMCM2000问题-B: 无线电信道分配AMCM2000问题-C：大象群落的兴衰AMCM2001问题- A: 选择自行车车轮AMCM2001问题-B：逃避飓风怒吼（一场恶风…）AMCM2001问题-C我们的水系-不确定的前景AMCM2002问题-A风和喷水池AMCM2002问题-B航空公司超员订票AMCM2002问题-C蜥蜴问题AMCM2003问题-A: 特技演员AMCM2003问题-C航空行李的扫描对策AMCM2004问题-A：指纹是独一无二的吗？AMCM2004问题-B：更快的快通系统AMCM2004问题-C：安全与否？AMCM2005问题-A：.水灾计划AMCM2005问题-B：TollboothsAMCM2005问题-C：.Nonrenewable ResourcesAMCM2006问题-A：用于灌溉的自动洒水器的安置和移动调度AMCM2006问题-B：通过机场的轮椅AMCM2006问题-C：在与HIV/爱滋病的战斗中的交易AMCM85问题-A 动物群体的管理在一个资源有限，即有限的食物、空间、水等等的环境里发现天然存在的动物群体。

1989 MCM A: The Midge Classification ProblemTwo species of midges, Af and Apf, have been identified by biologists Grogan and Wirth on the basis of antenna and wing length (see Figure 1). It is important to be able to classify a specimen as Af of Apf, given the antenna and wing length. Given a midge that you know is species Af or Apf, how would you go about classifying it?Apply your method to three specimens with (antenna, wing) lengths(1.24,1.80),(1.28,1.84),(1.40,2.04).Assume that the species is a valuable pollinator and species Apf is a carrier of a debilitating disease. Would you modify your classification scheme and if so, how? 两种蠓Af和Apf已由生物学家W.L.Grongan和W.W.Wirth（1981年）根据他们的触角长和翼长加以区分。

根据触角的长和翼长将标本分类是很重要的。

1、给你一只Af或者Apf的蝶，你怎样对它进行分类呢?2、用你的方法将翅膀、触角的长度分别为（1.24，1.80）（1.28，1.84）（1.40，2.04）的三个标本分类。

3、假设Af这个种类的是宝贵的传粉益虫，Apf确是传递令人衰弱的疾病的载体。

美国数学建模题目2017至2017翻译篇一：2017年建模美赛C题带翻译Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads.For example, in the Greater Seattle area drivers experience long delays during peak traffic hoursbecause the volume of traffic exceeds the designed capacity of the road networks. This is particularlypronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interestfor this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highwayswithout increasing number of lanes or roads. The behavior of these cars interacting with the existingtraffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving,cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (Seethe provided map and Excel spreadsheet).In particular, how do the effects change as thepercentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there atipping point where performance changes markedly? Under what conditions, if any, should lanes bededicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/oraverage traffic volume, and percentage of vehicles using self-driving, cooperating systems. Yourmodel should address cooperation between self-driving cars as well as the interaction between self-driving and non-self-driving vehicles. Your model should then be applied to the data for the roads ofinterest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to theGovernor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: Theappendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours. ? The nominal speed limit for all these roads is 60 miles per hour.? Mileposts are numbered from south to north, and west to east.? Lane widths are the standard 12 feet.? Highway 90 is classified as a state route until it intersects Interstate 5.? In case of any conflict between the data provided in this problem and any other source, use thedata provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。

Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads. For example, in the Greater Seattle area drivers experience long delays during peak traffic hours because the volume of traffic exceeds the designed capacity of the road networks. This is particularly pronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interest for this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highways without increasing number of lanes or roads. The behavior of these cars interacting with the existing traffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving, cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (See the provided map and Excel spreadsheet). In particular, how do the effects change as the percentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there a tipping point where performance changes markedly? Under what conditions, if any, should lanes be dedicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/or average traffic volume, and percentage of vehicles using self-driving, cooperating systems. Your model should address cooperation between self-driving cars as well as the interaction between self- driving and non-self-driving vehicles. Your model should then be applied to the data for the roads of interest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the Governor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: The appendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours.•The nominal speed limit for all these roads is 60 miles per hour.•Mileposts are numbered from south to north, and west to east.•Lane widths are the standard 12 feet.•Highway 90 is classified as a state route until it intersects Interstate 5.•In case of any conflict between the data provided in this problem and any other source, use the data provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。

A 题热水澡一个人进入浴缸洗澡放松。

浴缸的热水由一个水龙头放出。

然而浴缸不是一个可以水疗泡澡的缸，没有辅助加热系统和循环喷头，仅仅就是一个简单的盛水容器。

过一会，水温就会显著下降。

因此必须从热水龙头里面反复放水以加热水温。

浴缸的设计就是当水达到浴缸的最大容量，多余的水就会通过一个溢流口流出。

做一个有关浴缸水温的模型，从时间和地点两个方面来确定在浴缸中泡澡的人能采用的最佳策略，从而泡澡过程中能保持水温并在不浪费太多水的情况下使水温尽量接近最初的水温。

用你的模型来确定你的策略多大程度上依赖于浴缸的形状和容量，浴缸中的人的体型/体重/体温，以及这个人在浴缸中做出的动作。

如果这个人在最开始放水的时候加入了泡泡浴添加剂，这将会对你的模型结果有什么影响？要求提交一页MCM的总结，此外你的报告必须包括一页给浴缸用户看的非技术性的解释，其中描述了你的策略并解释了在泡澡过程中为什么保持平均的水温会非常困难。

B题太空垃圾地球轨道周围的小碎片的数量受到越来越多的关注。

据估计，目前大约有超过50万片太空碎片被视为是宇宙飞行器的潜在威胁并受到跟踪，这些碎片也叫轨道碎片。

2009年2月10号俄罗斯卫星科斯莫斯-2251与美国卫星iridium-33相撞的时候，这个问题在新闻媒体上就愈发受到广泛讨论。

已经提出了一些方法来清除这些碎片。

这些方法包括小型太空水流喷射器和高能量激光来瞄准具体的碎片，还有大型卫星来清扫碎片等等。

这些碎片数量和大小不一，有油漆脱离的碎片，也有废弃的卫星。

碎片高速转动使得定位清除变得困难。

建一个随时间变化的模型来确定一个最佳选择或组合的选择提供给一家私人公司让它以此为商业机遇来解决太空碎片问题。

你的模型应该包括对成本、风险、收益的定量和/或定性分析以及其他重要因素的分析。

你的模型应该既能够评估单个的选择也能够评估组合的选择，且能够探讨一些重要的”what if ”情景。

用你的模型来确定是否存在这样的机会，在经济上很有吸引力；或是根本不可能有这样的机会。

1987 MCM A: The Salt Storage ProblemFor approximately 15 years, a Midwestern state has stored salt used on roads in the winter in circular domes. Figure 1 shows how salt has been stored in the past. The salt is brought into and removed from the domes by driving front-end loaders up ramps of salt leading into the domes. The salt is piled 25 to 30 ft high, using the buckets on the front-end loaders.Recently, a panel determined that this practice is unsafe. If the front-end loader gets too close to the edge of the salt pile, the salt might shift, and the loader could be thrown against the retaining walls that reinforce the dome. The panel recommended that if the salt is to be piled with the use of the loaders, then the piles should be restricted to a matimum height of 15 ft.Construct a mathematical model for this situation and find a recommended maximum height for salt in the domes.大约15年来美国中西部的国家冬天在圆形空旷的地方储存盐。

PROBLEM A: The Keep-Right-Except-To-Pass Rule The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirementsbe needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part ofthe road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results ofyour earlier analysis?问题A ：除非超车否则靠右行驶的交通规则在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。

2010 MCMPROBLEM A: The Sweet SpotExplain the “sweet spot” on a baseball bat.Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.Some players believe that “corking” a bat (hollow ing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?A 最佳平衡点解释棒球棒上的“最佳平衡点”每一个击球手都知道在一根棒球棒的较宽部分有一个点，用该点击球时能够传递给球的力是最大的。

1985 年美国大学生数学建模竞赛MCM 试题1985年MCM:动物种群选择合适的鱼类和哺乳动物数据准确模型。

模型动物的自然表达人口水平与环境相互作用的不同群体的环境的重要参数,然后调整账户获取表单模型符合实际的动物提取的方法。

包括任何食物或限制以外的空间限制,得到数据的支持。

考虑所涉及的各种数量的价值,收获数量和人口规模本身,为了设计一个数字量代表的整体价值收获。

找到一个收集政策的人口规模和时间优化的价值收获在很长一段时间。

检查政策优化价值在现实的环境条件。

1985年MCM B:战略储备管理钴、不产生在美国,许多行业至关重要。

(国防占17%的钴生产。

1979年)钴大部分来自非洲中部,一个政治上不稳定的地区。

1946年的战略和关键材料储备法案需要钴储备,将美国政府通过一项为期三年的战争。

建立了库存在1950年代,出售大部分在1970年代初,然后决定在1970年代末建立起来,与8540万磅。

大约一半的库存目标的储备已经在1982年收购了。

建立一个数学模型来管理储备的战略金属钴。

你需要考虑这样的问题:库存应该有多大?以什么速度应该被收购?一个合理的代价是什么金属?你也要考虑这样的问题:什么时候库存应该画下来吗?以什么速度应该是画下来吗?在金属价格是合理出售什么?它应该如何分配?有用的信息在钴政府计划在2500万年需要2500万磅的钴。

美国大约有1亿磅的钴矿床。

生产变得经济可行当价格达到22美元/磅(如发生在1981年)。

要花四年滚动操作,和thsn六百万英镑每年可以生产。

1980年,120万磅的钴回收,总消费的7%。

1986 年美国大学生数学建模竞赛MCM 试题1986年MCM A:水文数据下表给出了Z的水深度尺表面点的直角坐标X,Y在码(14数据点表省略)。

深度测量在退潮。

你的船有一个五英尺的草案。

你应该避免什么地区内的矩形(75200)X(-50、150)?1986年MCM B:Emergency-Facilities位置迄今为止,力拓的乡牧场没有自己的应急设施。

美赛e题优秀论文翻译E题中文翻译：问题E：需要可持续城市！背景：许多社区正在实施智能增长计划，以考虑长期，可持续的规划目标。

“聪明的成长是关于帮助每个城镇和城市变得更加经济繁荣，社会公平和环境可持续的生活地方。

”[2]智能增长的重点是建设拥抱可持续发展的城市 - 经济繁荣，社会公平，环境可持续。

这个任务比以往任何时候都重要，因为世界正在迅速城市化。

预计到2050年，世界人口的66％将是城市人口 - 这将导致25亿人口被纳入城市人口。

[3]因此，城市规划变得越来越重要和必要，以确保人们获得公平和可持续的家园，资源和就业机会。

智能增长是一种城市规划理论，起源于1990年代，作为遏制城市持续蔓延和减少城市中心周围农田损失的手段。

智能增长的十大原则是[4]1混合土地利用2利用紧凑的建筑设计3创造一系列住房机会和选择4创建可步行的社区5培养独特的，有吸引力的社区，具有强烈的地方感6保留开放空间，农田，自然美景和关键环境区域7加强和指导现有社区的发展8提供多种交通选择9使开发决策具有可预测性，公平性和成本效益10鼓励社区和利益相关者在发展决策中进行合作这些广泛的原则必须适应社区的独特需求，才能有效。

因此，任何成功的衡量都必须包括一个城市的人口统计，增长需求和地理条件，以及坚持三个E的目标。

任务：国际城市管理集团（ICM）需要您帮助实施智能增长理论到世界各地的城市设计。

在两个不同的大陆选择两个中型城市（人口在10万和50万之间的任何城市）。

1.定义衡量城市智能增长成功率的指标。

它应该考虑可持续性的三个E和/或智能增长的十个原则。

2.研究选定城市的当前增长计划。

衡量和讨论每个城市目前的增长计划是否符合智能增长原则。

根据您的指标，当前的计划是否成功？3.使用智能增长原则在未来几十年内为两个城市制定增长计划。

支持您为什么根据您的城市的地理位置，预期增长率和经济机会选择您的计划的组件和计划。

使用您的指标评估您的智能增长计划的成功。

1991 MCM A: Water Tank Flow1991 MCM A: Water Tank FlowSome state water-right agencies require from communities data on the rate of water use, in gallons per hour, and the total amount of water used each day. Many communities do not have equipment to measure the flow of water in or out of the municipal tank. Instead, they can measure only the level of water in the tank, within 0.5% accuracy, every hour. More importantly, whenever the level in the tank drops below some minimum level L, a pump fills the tank up to the maximum level, H; however, there is no measurement of the pump flow either. Thus, one cannot readily relate the level in the tank to the amount of water used while the pump is working, which occurs once or twice per day, for a couple of hours each time. Estimate the flow out of the tank f(t) at all times, even when the pump is working, and estimate the total amount of water used during the day. Table 1 gives real data, from an actual small town, for one day[ table omitted]. The table gives the time, in, since the first measurement, and the level of water in the tank, in hundredths of a foot. For example, after 3316 seconds, the depth of water in the tank reached 31.10 feet. The tank is a vertical circular cylinder, with a height of 40 feet and a diameter of 57 feet. Usually, the pump starts filling the tank when the level drops to about 27.00 feet, and the pump stops when the level rises back to about 35.50 feet.1991 MCM B: The Steiner Tree Problem史坦纳树问题The cost for a communication line between two stations is proportional to the length of the line. The cost for conventional minimal spanning trees of a set of stations can often be cut by introducing “phantom” stations and then constructing a new Steiner tree. This device allows costs to be cut by up to 13.4% (= 1- sqrt(3/4)). Moreover, a network with n stations never requires more than n-2 points to construct the cheapest Steiner tree. Two simple cases are shown in Figure 1.For local networks, it often is necessary to use rectilinear or “checker-board” distances, instead of straight Euclidean lines. Distances in this metric are computed as shown in Figure 2.Suppose you wish to design a minimum costs spanning tree for a local network with 9 stations. Their rectangular coordinates are: a(0,15), b(5,20), c(16,24), d(20,20), e(33,25), f(23,11), g(35,7), h(25,0)i(10,3). You are restricted to using rectilinear lines. Moreover, all “phantom” stations must be located at lattice points (i.e., the coordinates must be integers). The cost for each line is its length.1.Find a minimal cost tree for the network.2.Suppose each stations has a cost w*d^(3/2), where d=degree of thestation. If w=1.2, find a minimal cost tree.3.Try to generalize this problem水箱流量一些水权协会向社区获取使用水的流动速率，每小时多少加能，和每天用水的总量。

1992 MCM A: Air-Traffic-Control Radar Power 空中交通雷达控制问题你将决定雷达在一个大型综合城市机场辐射的能量。

机场当局希望在减少雷达辐射能的情况下，保持安全与降低成本一致。

机场当局希望利用原有的高塔和接收电路系统。

为加大雷达使用度，唯一的选择就是：提升发送电路系统。

你所要回答的问题是：雷达必须释放多少能量以保证在离地100千米的高空飞行的普通客运机的检测。

1992 MCM B: Emergency Power Restoration紧急电力修复问题由于暴风雨的侵袭，沿海一带的电力公司必须有防控断电的应急系统。

这种系统要求：一输入数据，系统估算出修复所需的时间和成本，以及客观估算出由断电造成的损失。

在过去，夏威夷电力公司曾因为缺少这样一个优化项目被媒体抨击。

现在你是夏威夷电力公司的一名顾问。

HECO拥有一个电脑化的数据库和实时访问服务需要,目前需要以下的信息：报告的时间，报告者类型，受影响者人数估量，位置（x,y）.电力公司位于坐标轴的（0，0）和（40，40）之间，其中x,y的单位为米。

夏威夷电力公司的服务范围为-65 < x < 60 and -50 < y < 50。

该区域拥有优良的网络系统。

公司明确规定：在暴风雨离开之前，任何工作不得开始，除非求助区域是医院和铁路单位，这些区域需要立即处理如果工作人员可得到。

夏威夷电力公司聘用你制定客观评判标准并安排暴风雨后的修复工作。

要求见表1，人力资源见表2.注意：最早客户热线为4:20 A.M.暴风雨离开时间为6:00 A.M。

还要注意很多停电用户总是推迟才保修的。

夏威夷电力公司出自自身目的需要一份技术报告和一份用外行术语写的“执行简要“提交给新闻媒介。

另外，他们希望公众能为将来提供些建议。

为制定出你的优先计划安排系统，你还需做一些附加假设，并详细陈述这些假设。

PROBLEM A: The Leaves of a Tree"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:• Why do leaves have the various shapes that they have?为什么树叶会有不同的形状• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?是否叶与叶之间有最小的阴影（投影）以便于叶子最大面积的曝光？是否叶子量的分布以及枝干影响了它的形状？• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?说到树的形状，是否叶的形状与侧枝结构有关系？• How wou ld you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?如何评估一棵树的叶子数量？叶子的数量是否与树的尺寸有关系（比如高，密集度，量由形状决定）In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.除了你一个页面的汇总表，准备一页纸的信中列出您的主要结果的一个科学杂志的编辑PROBLEM B: Camping along the Big Long RiverVisitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so theonly way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings.大隆河（225公里）的游客可以享受美景和令人兴奋的白色湍急水流,这条河是无法去踏青，那么享受它的唯一途径是采取一河之旅，需要数天的露营。

美赛试题2009b试题B：This question involves the “energy” consequences of the cell phone revolution. Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones. What is the consequence of this in terms of electricity use? Every cell phone comes with a battery and a recharger.这个问题涉及到“能量”影响的手机革命，手机的使用量迅速增长，许多人正在使用手机来代替固定电话。

这方面的电力使用的结果是什么？每个手机配有一个电池和一个充电器。

Requirement 1Consider the current US, a country of about 300 million people. Estimate from available data the number H of households, with m members each, that in the past were serviced by landlines. Now, suppose that all the landlines are replaced by cell phones; that is, each of the m members of the household has a cell phone. Model the consequences of this change for electricity utilization in the current US, both during the transition and during the steady state. The analysis should take into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones (for example, the cell phones get lost and break).要求一目前认为美国是一个人口约有3亿人的国家，从现有数据估计家庭数为h，每个家庭有M个成员，以前是使用座机电话的。

PROBLEM A: Snowboard CourseDetermine the shape of a snowboard course (currently known as a “halfpipe”) to maximize the production of “vertical air” by a skilled snowboarder."Vertical air" is the maximum vertical distance above the edge of the halfpipe. Tailor the shape to optimize other possible requirements, such as maximum twist in the air.What tradeoffs may be required to develop a “practical” course?请设计一个单板滑雪场（现为“半管”或“U型池”）的形状，以便能使熟练的单板滑雪选手最大限度地产生垂直腾空。

“垂直腾空“是超出“半管”边缘以上的最大的垂直距离。

定制形状时要优化其他可能的要求，如：在空中产生最大的身体扭曲。

在制定一个“实用”的场地时哪些权衡因素可能需要？PROBLEM B: Repeater Coordinationfrequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available.How does your solution change if there are 10,000 users?Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.除了地理的分离、“连续编码音调控制系统”(CTCSS),有时被称为“私人专线”(PL)、通过这项技术可以减轻干扰问题。

1986 MCM A: Hydrographic（水道测量数的）Data（水文数据）The table below gives the depth Z of water in feet for surface points with rectangular coordinates（直角坐标系的）X, Y in yards（码数）[table of 14 data points omitted（遗漏的）]. The depth measurements were taken at low tide. Your ship hasa draft （【船舶学】吃水深度20. 【水文学】(水闸等的)出水道尺寸(或区域)，流水孔(或出水口)的大小21. (水轮机的)尾水管）of five feet. What region should you avoid within the rectangle (75,200) x (-50, 150)?下面这个表中给出了海洋深度Z和X，Y（以水平面为平面建立直角坐标）的相应数据（表中共有14组数据，以英尺为单位）。

深度是在海洋落潮时的测量值。

假设你的船有5英尺在矩形（75，200）x（-50，150）的范围内，你需要避免在什么区域内出现？1986 MCM B: Emergency-Facilities（紧急设施）LocationThe township( 镇区、小镇)of Rio Rancho has hitherto（迄今、到现在为止）not had its own emergency facilities. It has secured funds to erect two emergency facilities in 1986, each of which will combine ambulance, fire, and police services. Figure 1 indicates the demand [figure omitted], or number of emergencies per square block, for 1985. The “L” region in the north is an obstacle, while the rectangl e in the south is a part with shallow pond. It takes an emergency vehicle an average of 15 seconds to go one block in the N-S direction and 20 seconds in the E-W direction. Your task is to locate the two facilities so as to minimize the total response time. Assume that the demand is concentrated at the center of the block and that the facilities will be located on corners.Assume that the demand is uniformly distributed on the streets bordering each block and that the facilities may be located anywhere on the streets.在一个小镇上的里约农场迄今为止都没有自己的紧急设备。