美赛历年赛题及其翻译-推荐下载
美赛数学竞赛题目
有关“美赛数学竞赛”的题目
美赛数学竞赛的题目通常涉及多个数学领域，包括代数、几何、概率统计、微积分等。
这些题目通常要求参赛者具有扎实的数学基础和较强的分析能力，能够灵活运用数学知识解决实际问题。
有关“美赛数学竞赛”的题目示例如下：
题目：在一条直线上的n个点，可以构成多少条不同的线段？
这个问题涉及到组合数学的知识，需要参赛者通过分析和推理来找到答案。
具体而言，对于n个点，每两个点可以构成一条线段，所以总共可以构成C(n, 2) = n*(n-1)/2 条不同的线段。
需要注意的是，美赛数学竞赛的题目难度较大，需要参赛者具备较高的数学水平和较强的解题能力。
同时，在解题过程中还需要注意逻辑清晰、表达准确、符合数学规范等要求。
美赛历年赛题
美赛历年赛题
美国数学建模竞赛（MCM/ICM）自1985年创办以来已有35年的历史，每年都会发布三个模型问题供参赛选手在限定时间内进行研究和解答。
经过不断发展和完善，MCM/ICM成为了世界范围内最具影响力的数学建模竞赛之一。
以下是MCM/ICM历年来的一些典型赛题：
1985年 MCM A题：研究在给定经济情况下，如何规划BMW公司未来的生产计划及车型。
1987年 MCM A题：在地球上一个非常均匀的平面，建立一个小型城市，考虑各种环境因素如何影响城市的设施和功能。
1991年 MCM D题：分析社会上性别和种族歧视。
1997年 MCM C题：分析为什么珊瑚礁的污染问题比林区污染问题显得更为严重。
2002年 MCM A题：研究货轮舱位的装载问题，最大化收益同时保证船上货物负荷均衡。
2006年 MCM A题：建立模型研究地球大气环境中的水循环，探究人类活动对水循环的影响。
2010年 MCM A题：分析美国电力网络的可靠性，研究如何在自然灾害和人为故障的情况下使电力网络正常运作。
2014年 MCM A题：分析对于Fermi问题和经济增长的数学建模，探究经济增长的限制因素和未来发展趋势。
2018年 MCM A题：研究美国国家公园的野生动植物种类和数量变化，确定如何平衡保护野生动植物和国家公园的多个目的。
从这些题目中可以看出，MCM/ICM的竞赛内容涵盖了众多领域，如管理学、环保、气象、物流、生物学等等。
这不仅考验了参赛选手的数学建模水平，更需要他们具备良好的跨学科素养。
正是这种多学科交叉融合的特性，使得MCM/ICM成为了培养未来数学、理工科人才的重要平台之一。
美赛题目2024年中文题目
美赛题目2024年中文题目下载温馨提示:该文档是我店铺精心编制而成，希望大家下载以后，能够帮助大家解决实际的问题。
文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by theeditor. I hope that after you download them,they can help yousolve practical problems. The document can be customized andmodified after downloading,please adjust and use it according toactual needs, thank you!In addition, our shop provides you with various types ofpractical materials,such as educational essays, diaryappreciation,sentence excerpts,ancient poems,classic articles,topic composition,work summary,word parsing,copy excerpts,other materials and so on,want to know different data formats andwriting methods,please pay attention!【标题】2024年美赛（MCM/ICM）中文题目解析与展望【正文】美赛，全称为美国数学建模竞赛（Mathematical Contest in Modeling / Interdisciplinary Contest in Modeling），是全球影响力最大的数学建模竞赛之一。
美赛 历年统计类赛题
美赛历年统计类赛题
美赛是指美国大学生数学建模竞赛，是一个涉及数学、统计、
计算机等多个学科的综合性竞赛。
历年的统计类赛题涉及了各种各
样的问题，涵盖了经济、环境、医学、社会等多个领域。
以下是一
些历年美赛统计类赛题的主题和问题：
1. 一年中的能源消耗，要求分析某个地区一年中的能源消耗情况，包括电力、煤气、汽油等各种能源的使用情况，并预测未来的
能源需求。
2. 流感传播模型，要求建立数学模型来描述流感在人群中的传
播规律，包括传染率、潜伏期等参数的估计和预测。
3. 交通拥堵问题，要求分析城市中交通拥堵的原因和影响因素，提出改善交通状况的方案，并对方案的效果进行评估。
4. 医疗资源分配，要求设计合理的医疗资源分配方案，包括医
院的选址、医生的分配等，以最大化医疗资源的利用效率。
5. 森林火灾预测，要求建立森林火灾的预测模型，包括气象条
件、地形因素等对火灾发生的影响，以及对未来火灾的概率预测。
以上仅是一些例子，美赛的统计类赛题涉及的范围非常广泛，涵盖了社会生活的方方面面。
参赛者需要在有限的时间内，应用数学和统计知识，解决实际问题，并撰写完整的论文报告。
这些赛题旨在培养学生的综合分析和解决实际问题的能力，对参赛者的综合素质要求很高。
年美赛d题题目翻译
问题D：优化机场安全检查站乘客吞吐量继2001年9月11日美国发生恐怖袭击事件后，全世界的机场安全状况得到显着改善。
机场有安全检查站。
在那里，乘客及其行李被检查爆炸物和其他危险物品。
这些安全措施的目的是防止乘客劫持或摧毁飞机，并在旅行期间保持所有乘客的安全。
然而，航空公司有既得利益，通过最小化他们在安全检查站排队等候并等待他们的航班的时间，来保持乘客积极的飞行体验。
因此，在最大化安全性和最小化对乘客的不便之前存在对立。
在2016年，美国运输安全局（TSA）受到了对极长线路，特别是在芝加哥的奥黑尔国际机场的尖锐批评。
在此公众关注之后，TSA投资对其检查点设备和程序进行了若干修改，并增加了在高度拥堵的机场中的人员配置。
虽然这些修改在减少等待时间方面有一定的成功，但TSA在实施新措施和增加人员配置方面花费了多少成本尚不清楚。
除了在奥黑尔机场的问题，还有在其他机场，包括通常排队等待时间较短的机场，会出现不明原因和不可预测的排队拥挤情况的事件。
检查点排队状况的这种高度变化性对于乘客来说可能是极其不利的，因为他们面临着不必要地早到达或可能赶不上他们的预定航班的风险。
许多新闻文章，包括[1,2,3,4,5]，描述了与机场安全检查站相关的一些问题。
您的内部控制管理（ICM）团队已经与TSA签订合同，审查机场安全检查站和人员配置，以确定潜在的干扰乘客吞吐量的瓶颈。
他们特别感兴趣的解决方案是，既增加检查点吞吐量，减少等待时间的变化，同时保持相同的安全和安全标准。
美国机场安全检查点的当前流程如图1所示。
区域A：乘客随机到达检查站，并等待队列，直到安全人员可以检查他们的身份证明和登机文件。
区域B：然后乘客移动到打开检查的队列;根据机场的预期活动水平，可能开放更多或更少的线路。
一旦乘客到达这个队列的前面，他们准备所有的物品用于X射线检查。
乘客必须去除鞋子，皮带，夹克，金属物体，电子产品和带液体容器，将它们放置在单独的X射线箱中;笔记本电脑和一些医疗设备也需要从其袋中取出并放置在单独的容器中。
美赛历年题目_pdf
马剑整理历年美国大学生数学建模赛题目录MCM85问题-A 动物群体的管理 (3)MCM85问题-B 战购物资储备的管理 (3)MCM86问题-A 水道测量数据 (4)MCM86问题-B 应急设施的位置 (4)MCM87问题-A 盐的存贮 (5)MCM87问题-B 停车场 (5)MCM88问题-A 确定毒品走私船的位置 (5)MCM88问题-B 两辆铁路平板车的装货问题 (6)MCM89问题-A 蠓的分类 (6)MCM89问题-B 飞机排队 (6)MCM90-A 药物在脑内的分布 (6)MCM90问题-B 扫雪问题 (7)MCM91问题-B 通讯网络的极小生成树 (7)MCM 91问题-A 估计水塔的水流量 (7)MCM92问题-A 空中交通控制雷达的功率问题 (7)MCM 92问题-B 应急电力修复系统的修复计划 (7)MCM93问题-A 加速餐厅剩菜堆肥的生成 (8)MCM93问题-B 倒煤台的操作方案 (8)MCM94问题-A 住宅的保温 (9)MCM 94问题-B 计算机网络的最短传输时间 (9)MCM-95问题-A 单一螺旋线 (10)MCM95题-B A1uacha Balaclava学院 (10)MCM96问题-A 噪音场中潜艇的探测 (11)MCM96问题-B 竞赛评判问题 (11)MCM97问题-A Velociraptor(疾走龙属)问题 (11)MCM97问题-B为取得富有成果的讨论怎样搭配与会成员 (12)MCM98问题-A 磁共振成像扫描仪 (12)MCM98问题-B 成绩给分的通胀 (13)MCM99问题-A 大碰撞 (13)MCM99问题-B “非法”聚会 (14)MCM2000问题-A空间交通管制 (14)MCM2000问题-B: 无线电信道分配 (14)MCM2001问题- A: 选择自行车车轮 (15)MCM2001问题-B 逃避飓风怒吼（一场恶风...） .. (15)MCM2001问题-C我们的水系-不确定的前景 (16)MCM2002问题-A风和喷水池 (16)MCM2002问题-B航空公司超员订票 (16)MCM2002问题-C (16)MCM2003问题-A: 特技演员 (18)MCM2003问题-B: Gamma刀治疗方案 (18)MCM2003问题-C航空行李的扫描对策 (19)MCM2004问题-A：指纹是独一无二的吗？ (19)MCM2004问题-B：更快的快通系统 (19)MCM2004问题-C安全与否？ (19)MCM2005问题A.水灾计划 (19)MCM2005B.Tollbooths (19)MCM2005问题C：不可再生的资源 (20)MCM2006问题A: 用于灌溉的自动洒水器的安置和移动调度 (20)MCM2006问题B: 通过机场的轮椅 (20)MCM2006问题C : 抗击艾滋病的协调 (21)MCM2007问题B ：飞机就座问题 (24)MCM2007问题C：器官移植：肾交换问题 (24)MCM2008问题A:给大陆洗个澡 (28)MCM2008问题B：建立数独拼图游戏 (28)MCM85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。
美赛历年题目汇总
美赛历年题目汇总
以下是美赛历年的一些题目汇总：
2018年的题目是“多跳HF无线电传播语言传播趋势”；
2017年的题目是“管理赞比西河高速路收费合并”；
2016年的题目是“浴缸的水温模型解决空间碎片问题”；
2015年的题目是“根除病毒寻找失踪的飞机”；
2014年的题目是“(交通流、路况)优化(体育教练)综合评价”；
2013年的题目是“平底锅受热，热力学、几何(大模型解答所有题目)，可利用淡水资源的匮乏，(水资源)预测、最优化”；
2012年的题目是“一棵树的叶子沿着BigLongRiver野营，(流程)优化”；
需要注意的是，这里只列出了部分美赛历年的题目，而且每年的题目都可能有所不同。
同时，美赛赛题的难度较高，需要具备一定的数学建模和计算机编程能力。
因此，在参加美赛前，建议充分准备，提高自己的数学建模和计算机编程能力。
2020美赛E题参考翻译
2020ICM 周末1问题E ：塑料溺水自20世纪50年代以来，塑料的制造因其多种用途而成倍增长，如食品包装、消费品、医疗器械和建筑。
虽然有很大的好处，但增加塑料生产的负面影响是令人关切的。
塑料产品不容易分解，很难处理，只有大约9%的塑料被回收[1]，每年进入海洋的大约4-1200万吨塑料废物可以看到效果[1，2]。
塑料废物具有严重的环境后果，据预测，如果我们目前的趋势继续下去，到2050年，海洋中的塑料含量将超过鱼类[2]。
对海洋生物的影响已被研究[3]，但对人类健康的影响尚未完全理解[4]单一用途和一次性塑料产品的兴起导致了致力于制造塑料废物的整个行业。
它还表明，产品有用的时间远远短于适当减少塑料浪费所需的时间。
因此，为了解决塑料废物问题，我们需要减缓塑料生产的速度，改进我们管理塑料废物的方法。
..您的团队已被国际塑料废物管理理事会（ICM ）雇用，以解决这一不断升级的环境危机。
你必须制定一个计划，以显著减少，如果不消除，一次性使用和一次性塑料产品的浪费..∙开发一个模型，以估计单一用途或一次性塑料产品废物的最大水平，这些废物可以安全地减轻，而不会造成进一步的环境损害。
在许多因素中，您可能需要考虑这种废物的来源、当前废物问题的程度以及处理废物的资源的可用性。
∙讨论在多大程度上可以减少塑料废物，以达到环境安全水平。
这可能涉及考虑影响塑料废物水平的因素，包括但不限于单一用途或一次性塑料的来源和用途、塑料替代品的可用性、对公民生活的影响，或城市、区域、国家和大陆减少单一用途或一次性塑料的政策，以及此类政策的有效性。
这些因素可能因地区而异，因此考虑到特定区域的制约因素可能会使某些政策比其他政策更有效。
∙利用你的模型和讨论，为单一用途或一次性塑料产品的全球废物的最低可达到水平设定一个目标，并讨论实现这一水平的影响。
你可以考虑改变人类生活的方式，环境影响，或对数万亿美元塑料工业的影响。
∙虽然这是一个全球性问题，但其原因和影响在各国或各区域之间并不平等分布。
美赛历年题目2005—2013
MCM 2013 A题：最佳巧克力蛋糕烤盘当你使用一个矩形的烤盘烘烤食物时，热量会集中在烤盘的四个角落，于是角落处的食物就会被烤糊（烤盘边缘处也有类似情形，但程度轻一些）。
当使用一个圆形烤盘时，热量会均匀地分布在整个边缘上，就不会再有边缘上烤糊的现象发生。
然而，由于大多数烤箱内部是矩形的，如果使用圆形烤盘，就不能充分利用烤箱的内部空间了。
建立一个模型，来描述热量在不同形状的烤盘表面的分布。
这些形状包括矩形、圆形以及两者之间的过渡形状。
假设，1、矩形烤箱的宽长比为 W/L。
2、每个烤盘的面积为A。
3、先考虑烤箱内有两个搁架且间隔均匀的情形。
建立一个模型用以选择满足下列条件的最佳烤盘的形状：(1)、使得烤箱中可以容纳的烤盘数量(N)最大。
(2)、使得烤盘上的热量分布(H)最均匀。
3、综合(1)、(2)两个条件，并且为(1)、(2)分别设置权值p和(1-p)，寻求最优。
然后描述结果随着 W/L 和 p 的值的变化是如何变化的。
除了撰写 MCM 论文之外，你还要为新的一期巧克力蛋糕美食杂志准备一个一至两页的广告，阐述你的设计和结果的亮点所在。
MCM 2013 B题：水，水，无处不在淡水资源是世界上许多地方持续发展的限制因素。
建立数学模型来确定一个有效的，可行的，低成本的2013年用水计划，来满足某国(从下方的列表中选择一个国家)未来(2025年)的用水需求，并确定最优的淡水分配计划。
特别的，你的数学模型必须包括储存、运输、淡化和节水等环节。
如果可能的话，用你的模型来讨论你的计划对经济，自然和环境的影响。
提供一个非技术性的意见书给政府领导概述你的方法，以及方法的可行性和成本，以及它为什么是“最好的用水计划的选择”。
国家：美国、中国、俄罗斯、埃及或者沙特阿拉伯。
ICM 2013 C题：地球健康的网络建模背景：全社会都在关注如何研究与应用模型来预测我们地球的生物和环境的健康状况。
许多科学研究表明地球的环境和生物系统所面对的压力正在增加,但是能够验证这一观点的全局性模型却很少。
85-09历年美赛（MCM）中文试题
85-09历年美赛（MCM）中文试题校苑资源网整理历年美国大学生数学建模赛题目录MCM85问题-A 动物群体的管理.............................................................................................- 3 - MCM85问题-B 战购物资储备的管理.....................................................................................- 3 - MCM86问题-A 水道测量数据.................................................................................................- 4 - MCM86问题-B 应急设施的位置.............................................................................................- 4 - MCM87问题-A 盐的存贮.........................................................................................................- 5 - MCM87问题-B 停车场.............................................................................................................- 5 - MCM88问题-A 确定毒品走私船的位置.................................................................................- 5 - MCM88问题-B 两辆铁路平板车的装货问题.........................................................................- 6 - MCM89问题-A 蠓的分类.........................................................................................................- 6 - MCM89问题-B 飞机排队.........................................................................................................- 6 - MCM90问题 A 药物在脑内的分布.........................................................................................- 6 - MCM90问题-B 扫雪问题.........................................................................................................- 7 - MCM91问题-B 通讯网络的极小生成树.................................................................................- 7 - MCM 91问题-A估计水塔的水流量........................................................................................- 7 - MCM92问题-A 空中交通控制雷达的功率问题.....................................................................- 7 - MCM 92问题-B 应急电力修复系统的修复计划....................................................................- 7 - MCM93问题-A 加速餐厅剩菜堆肥的生成.............................................................................- 8 - MCM93问题-B 倒煤台的操作方案.........................................................................................- 8 - MCM94问题-A 住宅的保温.....................................................................................................- 9 - MCM 94问题-B 计算机网络的最短传输时间........................................................................- 9 - MCM-95问题-A 单一螺旋线..................................................................................................- 10 - MCM95问题-B A1uacha Balaclava 学院................................................................................- 10 - MCM96问题-A 噪音场中潜艇的探测...................................................................................- 11 - MCM96问题-B 竞赛评判问题...............................................................................................- 11 - MCM97问题-A Velociraptor(疾走龙属)问题..........................................................................- 11 - MCM97问题-B 为取得富有成果的讨论怎样搭配与会成员................................................- 12 - MCM98问题-A 磁共振成像扫描仪.......................................................................................- 12 - MCM98问题-B 成绩给分的通胀...........................................................................................- 13 - MCM99问题-A 大碰撞...........................................................................................................- 13 - MCM99问题-B “非法”聚会...............................................................................................- 14 - MCM2000问题-A 空间交通管制............................................................................................- 14 - MCM2000问题-B: 无线电信道分配......................................................................................- 14 -MCM2001问题- A: 选择自行车车轮.....................................................................................- 15 - MCM2001问题-B 逃避飓风怒吼（一场恶风…）...............................................................- 15 - MCM2001问题-C我们的水系-不确定的前景.......................................................................- 16 - MCM2002问题-A风和喷水池................................................................................................- 16 - MCM2002问题-B航空公司超员订票....................................................................................- 16 - MCM2002问题-C 蜥蜴问题...................................................................................................- 16 - MCM2003问题-A: 特技演员..................................................................................................- 18 - MCM2003问题-B: Gamma刀治疗方案.................................................................................- 18 - MCM2003问题-C航空行李的扫描对策................................................................................- 19 - MCM2004问题-A：指纹是独一无二的吗？.........................................................................- 19 - MCM2004问题-B：更快的快通系统.....................................................................................- 19 - MCM2004问题-C安全与否？................................................................................................- 19 - MCM2005问题 A.水灾计划....................................................................................................- 19 - MCM2005问题 B 收费站问题...............................................................................................- 19 - MCM2005问题C：不可再生的资源.....................................................................................- 20 - MCM2006问题A: 用于灌溉的自动洒水器的安置和移动调度..........................................- 20 - MCM2006问题B: 通过机场的轮椅......................................................................................- 20 - MCM2006问题C : 抗击艾滋病的协调.................................................................................-21 - MCM2007 问题A：不公正的选区划分................................................................................- 23 - MCM2007 问题B：飞机就座问题........................................................................................- 24 - ICM2007 问题C：器官移植：肾交换问题...........................................................................- 24 - MCM2008问题A:给大陆洗个澡............................................................................................- 27 - MCM2008问题B：建立数独拼图游戏.................................................................................- 27 - ICM 2008问题C：寻找好的卫生保健系统...........................................................................- 27 - MCM2009 问题 A 设计一个交通环岛..................................................................................- 28 - MCM2009问题B 能源和手机...............................................................................................- 28 - ICM2009问题C 构建食物系统: 重新平衡被人类影响的生态系统...................................- 29 -校苑数学建模论坛整理MCM85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。
美赛e题优秀论文翻译
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。
数模1998-2016年历年美赛题目(中文)
2016 年美赛题目翻译Program A一个人用热水从一个水龙头里灌满一个浴缸，然后安顿在浴缸中，清洗和放松。
不幸的是，浴缸不是一个温泉式浴缸，一个二次加热系统和循环射流，而是一个简单的水容器。
过了一会儿，洗澡就明显地凉快，所以人增加了一个恒定滴热水从水龙头加热洗浴用水。
该浴缸的设计是在这样一种方式，当浴缸达到容量，多余的水通过溢流泄流。
在空间和时间上开发一个浴缸的水的温度模型，以确定最佳的策略，在浴缸的人可以采取保持温度，即使在整个浴缸和尽可能接近的初始温度，没有浪费太多的水。
使用你的模型来确定你的策略取决于浴缸的形状和体积，浴缸的形状/体积/温度，浴缸中的人的运动。
如果这个人用了一个泡泡浴剂，而最初填充浴缸，以协助清洗，这会影响你的模型的结果？除了要求的一页摘要MCM提交，你的报告必须包括一一页的非技术性解释的浴缸，描述你的策略，解释为什么它是如此难以在洗澡水温度得到均匀地保持用户Program B小碎片在轨道上绕地球金额已日益受到关注。
据估计，超过50万件的空间碎片，也被称为轨道碎片，目前都正在跟踪的潜在危害飞船。
这个问题本身在新闻媒体上变得更广泛的讨论时，俄罗斯卫星的Kosmos-2251和美国铱卫星-33 2009年2月10日，上相撞。
已经提出许多方法以除去碎屑。
这些方法包括小的，基于空间的水射流，并用于针对碎片的特定部分高能激光器和大型卫星，旨在清扫杂物，等等。
碎片的大小和质量范围从漆片的废弃卫星。
碎片“高速轨道捕获做出困难。
开发时间依赖模型来确定一个私人公司可以采取作为一个商业机会，以解决空间碎片问题的替代品的最佳替代品或组合。
您的模型应该包括成本，风险，收益定量和/或定性的估计，以及其他的重要因素。
您的模型应该能够评估独立的替代方案以及替代品的组合，并能够探索各种重要的“如果什么？”的情景。
使用你的模型，确定经济上有吸引力的机会是否存在没有这样的机会是可能的。
如果可行的商业机会的存在作为替代的解决方案，提供了用于去除碎屑的不同选项的比较，并包括特定建议作为对碎片应如何除去。
美赛历年题目
具体可以登录官网看/undergraduate/contests/matrix/index.html2014 MCM ProblemsPROBLEM A: 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 arepassing 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 requirements be 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 of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?PROBLEM B: College Coaching LegendsSports Illustrated, a magazine for sports enthu siasts, is looking for the “best all time college coach” male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your model’s top 5 coaches in each of 3 different sports.In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand.Problem AProblem: Unloading Commuter TrainsTrains arrive often at a central Station, the nexus for many commuter trains from suburbs of larger cities on a “commuter” line. Most trains are long (perhaps 10 or more cars long). The distance a passenger has to walk to exit the train area is quite long. Each train car has only two exits, one near each end so that the cars can carry as many people as possible. Each train car has a center aisle and there are two seats on one side and three seats on the other for each row of seats.To exit a typical station of interest, passengers must exit the car, and then make their way to a stairway to get to the next level to exit the station. Usually these trains are crowded so there is a “fan” of passengers from the train trying to get up the stairway. The stairway could accommodate two columns of people exiting to the top of the stairs.Most commuter train platforms have two tracks adjacent to the platform. In the worst case, if two fully occupied trains arrived at the same time, it might take a long time for all the passengers to get up to the main level of the station.Build a mathematical model to estimate the amount of time for a passenger to reach the street level of the station to exit the complex. Assume there are n cars to a train, each car has length d. The length of the platform is p, and the number of stairs in each staircase is q.Use your model to specifically optimize (minimize) the time traveled to reach street level to exit a station for the following:Requirement 1.One fully occupied train’s passengers to exit the train, and ascend the stairs to reach the street access level of the stationRequirement 2.Two fully occupied trains’ passengers (all passengers exit onto a common platform) to exit the trains, and ascend the stairs to reach the street access level of the station.Requirement 3. If you could redesign the location of the stairways along the platform, where should these stairways be placed to minimize the time for one or two trains’ passengers to exit the station?Requirement 4. How does the time to street level vary with the number s of stairways that one builds?Requirement 5. How does the time vary if the stairways can accommodate k people, k an integer greater than one?In addition to the HiMCM format, prepare a short non-technical article to the director of transportation explaining why they should adopt your model to improve exiting a station.Problem BProblem: The Next Plague?In 2014, the world saw the infectious Ebola virus spreading in western Africa. Throughout human history, epidemics have come and gone with some infecting and/or killing thousands and lasting for years and others taking less of a human toll. Some believe these events are just nature’s way of controlling the growth of a species while others think they could be a conspiracy or deliberate act to cause harm. This problem will most likely come down to how to expend (or not expend) scarce resources (doctors, containment facilities, money, research, serums, etc…) to deal with a crisis.Situation: A routine humanitarian mission on an island in Indonesia reported a small village where almost half of its 300 inhabitants are showing similar symptoms. In the past week, 15 of the “infected” have died. This village is known to trade with nearby villages and other islands. Your modeling team works for a major center of disease control in the capital of your country (or if you prefer, for the International World Health Organization).Requirement 1: Develop a mathematical model(s) that performs the following functions as well as how/when to best allocate these scarce resources and…• Determines and classifies the type and severity of the spread of the disease• Determines if an epidemic is contained or not• Triggers appropriate measures (when to treat, when to transport victims, when to restrict movement, when to let a disease run its co urse, etc…) to contain a disease Note: While you may want to start with the well-known “SIR” family of models for parts of this problem, consider others, modifications to the SIR, multiple models, or creating your own.Requirement 2: Based on the information given, your model, and the assumptions your team has made, what initial recommendations does your team have for your country’s center for disease control? (Give 3-5 recommendations with justifications)Additional Situational Information: A multi-nationa l research team just returned to your country’s capital after spending 7 days gathering information in the infected village.Requirement 3: You can ask them up to 3 questions to improve your model. What would you ask and why?Additional Situational Information: The multi-national research team concluded that the disease:• Appears to spread through contact with bodily fluids of an infected person• The elderly and children are more likely to die if infected• A nearby island is starting to s how similar signs of infection• One of the researchers that returned to your capital appears infectedRequirement 4: How does the additional information above change/modify your model? Requirement 5: Write a one-page synopsis of your findings for your local non-technical news outlet.2013 MCM ProblemsPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven. Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.Assume1. A width to length ratio of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced.Develop a model that can be used to select the best type of pan (shape) under the following conditions:1. Maximize number of pans that can fit in the oven (N)2. Maximize even distribution of heat (H) for the pan3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different valuesof W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.PROBLEM B: Water, Water, EverywhereFresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, andcost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outlining your approach, its feasibility and costs, and why it is the “best water strategy choice.”Countries: United States, China, Russia, Egypt, or Saudi Arabia2013 ICM ProblemNetwork Modeling of Earth's HealthBackground: Society is interested in developing and using models to forecast thebiological and environmental health conditions of our planet. Many scientific studieshave concluded that there is growing stress on Earth's environmental and biologicalsystems, but there are very few global models to test those claims. The UN-backedMillennium Ecosystem Assessment Synthesis Report found that nearly two-thirds ofEarth's life-supporting ecosystems— including clean water, pure air, and stableclimate— are being degraded by unsustainable use. Humans are blamed for much ofthis damage. Soaring demands for food, fresh water, fuel, and timber have contributedto dramatic environmental changes; from deforestation to air, land, and water pollution.Despite the considerable research being conducted on local habitats and regionalfactors, current models do not adequately inform decision makers how their provincialpolices may impact the overall health of the planet. Many models ignore complex globalfactors and are unable to determine the long-range impacts of potential policies. While scientists realize that the complex relationships and cross-effects in myriadenvironmental and biological systems impact Earth's biosphere, current models oftenignore these relationships or limit the systems' connections. The system complexitiesmanifest in multiple interactions, feedback loops, emergent behaviors, and impendingstate changes or tipping points. The recent Nature article written by 22 internationallyknown scientists entitled "Approaching a state shift in Earth's biosphere" outlines manyof the issues associated with the need for scientific models and the importance ofpredicting potential state changes of the planetary health systems. The article providestwo specific quantitative modeling challenges in their call for better predictive models:1) To improve bio-forecasting through global models that embrace the complexityof Earth's interrelated systems and include the effects of local conditions on theglobal system and vice versa.2) To identify factors that could produce unhealthy global state-shifts and to showhow to use effective ecosystem management to prevent or limit these impendingstate changes.The resulting research question is whether we can build global models using local or regional components of the Earth's health that predict potential state changes and help decision makers design effective policies based on their potential impact on Earth's health. Although many warning signs are appearing, no one knows if Planet Earth is truly nearing a global tipping point or if such an extreme state is inevitable.The Nature article and many others point out that there are several important elements at work in the Earth's ecosystem (e.g., local factors, global impacts, multi-dimensional factors and relationships, varying time and spatial scales). There are also many other factors that can be included in a predictive model — human population, resource and habitat stress, habitat transformation, energy consumption, climate change, land use patterns, pollution, atmospheric chemistry, ocean chemistry, bio diversity, and political patterns such as social unrest and economic instability. Paleontologists have studied and modeled ecosystem behavior and response during previous cataclysmic state shifts and thus historic-based qualitative and quantitative information can provide background for future predictive models. However, it should be noted that human effects have increased significantly in our current biosphere situation.Requirements:You are members of the International Coalition of Modelers (ICM) which will soon be hosting a workshop entitled "Networks and Health of Planet Earth" and your research leader has asked you to perform modeling and analysis in advance of the workshop.He requires your team to do the following:Requirement 1: Build a dynamic global network model of some aspect of Earth'shealth (you develop the measure) by identifying local elements of this condition (network nodes) and appropriately connecting them (network links) to track relationship and attribute effects. Since the dynamic nature of these effects is important, this network model must include a dynamic time element that allows the model to predict future states of this health measure. For example, your nodes could be nations, continents, oceans, habitats, or any combination of these or other elements which together constitute a global model. Your links could represent nodal or environmental influences, or the flow or propagation of physical elements (such as pollution) over time. Your health measure could be any element of Earth's condition to include demographic, biological, environmental, social, political, physical, and/or chemical conditions. Besure to define all the elements of your model and explain the scientific bases for your modeling decisions about network measures, nodal entities, and link properties. Determine a methodology to set any parameters and explain how you could test your model if sufficient data were available. What kinds of data could be used to validate or verify the efficacy of your model? (Note: If you do not have the necessary data to determine parameters or perform verification, do not throw out the model. Your supervisor realizes that, at this stage, good creative ideas and theories are as important as verified data-based models.) Make sure you include the human element in yourmodel and explain where human behavior and government policies could affect theresults of your model.Requirement 2: Run your model to see how it predicts future Earth health. You mayneed to estimate parameters that you would normally determine from data. (Remember, this is just to test and understand the elements of your model, not to use itfor prediction or decision making.) What kinds of factors will your model produce?Could it predict state change or tipping points in Earth's condition? Could it provide warning about global consequences of changing local conditions? Could it informdecision makers on important policies? Do you take into account the human elementsin your measures and network properties?Requirement 3: One of the powerful elements of using network modeling is the abilityto analyze the network structure. Can network properties help identify critical nodes or relationships in your model? If so, perform such analysis. How sensitive is your modelto missing links or changing relationships? Does your model use feedback loops ortake into account uncertainties? What are the data collection issues? Does yourmodel react to various government policies and could it thus help inform planning? Requirement 4: Write a 20-page report (summary sheet does not count in the 20pages) that explains your model and its potential. Be sure to detail the strengths and weaknesses of the model. Your supervisor will use your report as a major theme in the upcoming workshop and, if it is appropriate and insightful to planetary health modeling,will ask you to present at the upcoming workshop. Good luck in your network modeling work!Potentially helpful references include:Anthony D. Barnosky, Elizabeth A. Hadly, Jordi Bascompte, Eric L. Berlow, James H. Brown, Mikael Fortelius, Wayne M. Getz, John Harte, Alan Hastings, Pablo A. Marquet, Neo D. Martinez, Arne Mooers, Peter Roopnarine, Geerat Vermeij, John W. Williams, Rosemary Gillespie, Justin Kitzes, Charles Marshall, Nicholas Matzke, David P. Mindell, Eloy Revilla, Adam B. Smith. "Approaching a state shift in Earth's biosphere,". Nature, 2012; 486 (7401): 52 DOI: 10.1038/nature11018Donella Meadows, Jorgen Randers, and Dennis Meadows. Limits to Growth: The 30-year update, 2004.Robert Watson and A.Hamid Zakri. UN Millennium Ecosystem Assessment Synthesis Report, United Nations Report, 2005.University of California - Berkeley. "Evidence of impending tipping point for Earth." ScienceDaily, 6 Jun. 2012. Web. 22 Oct. 2012.2012 MCM ProblemsPROBLEM 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?• 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?• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?• How would 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)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.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 the only 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 yourone page summary sheet, prepare a one page memo to the managers of the river describing your key findings.2011 MCM ProblemsPROBLEM 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?PROBLEM B: Repeater CoordinationThe VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by “repeaters,” which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.In addition to geographical separation, the “continuous tone-coded squelch sy stem” (CTCSS), sometimes nicknamed “private line” (PL), technology can be used to mitigate interference problems. This system associates to each repeater a separate subaudible tone that is transmitted by all users who wish to communicate through that repeater. The repeater responds only to received signals with its specific PL tone. With this system, two nearby repeaters can share the same frequency pair (for receive and transmit); so more repeaters (and hence more users) can be accommodated in a particular area.For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency 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.。
美赛题目2010-2018（含目录）
目录2018 年美赛题目翻译 (3)问题A：多跳HF 无线电传播 (3)问题B：语言传播趋势 (3)问题C ：能源配置与预测 (5)问题D：从汽油驾驶到E （电）驾驶 (6)问题E：气候变化如何影响区域不稳定？ (7)问题F：隐私成本问题 (8)2017 年美赛题目翻译 (10)问题A：管理赞比西河 (10)问题B：收费后合并 (11)问题C：“合作和导航” (12)问题D：在机场安全检查站优化乘客吞吐量 (13)问题E：规划可持续城市的发展 (15)问题F：迁移到火星：2100城市社会的乌托邦劳动力 (17)2016 年美赛题目翻译 (20)Program A 浴缸的水温模型 (20)Program B 解决空间碎片问题 (20)Program C 优质基金挑战 (21)2015 年美赛题目翻译 (21)问题一：根除病毒 (21)问题B：寻找失踪的飞机 (22)2014 年美赛题目翻译 (22)问题A：（交通流、路况）优化 (22)问题B：（体育教练）综合评价 (23)2013 年美赛题目翻译 (23)A ：平底锅受热 (23)B：可利用淡水资源的匮乏 (24)2012 年美赛题目翻译 (25)A 题：一棵树的叶子 (25)B：沿着 Big Long River 野营 (25)2011 年美赛题目翻译 (26)A:单板滑雪场地 (26)B：中继站的协调 (26)2010 年美赛题目翻译 (27)A 题：解释棒球棒上的“最佳击球点” (27)B 题系列犯罪地理效应 (27)2018年美赛题目翻译问题A：多跳HF 无线电传播背景：在高频段（HF,定义为3-10MHz），无线电波可以在地球表面和电离层之间的多次反射以进行长距离的传输（从地球表面上的一个点到地球表面上的另一个远点）。
对于低于最大可用频率（MUF）的频率，来自地面源的HF 无线电波将随着每个连续的跳跃继续前进从电离层反射回地球，在那里它们可能再次反射回到电离层，也可能再次反射回地球，等等。
美赛历年赛题及其翻译-推荐下载
2015年：A题一个国际性组织声称他们研发出了一种能够阻止埃博拉，并治愈隐性病毒携带者的新药。
建立一个实际、敏捷、有效的模型，不仅考虑到疾病的传播、药物的需求量、可能的给药措施、给药地点、疫苗或药物的生产速度，而且考虑你们队伍认为重要的、作为模型一部分的其他因素，用于优化埃博拉的根除，或至少缓解目前（治疗）的紧张压力。
除了竞赛需要的建模方案以外，为世界医学协会撰写一封1-2页的非技术性的发言稿，以便其公告使用。
B题回顾马航MH370失事事件。
建立一个通用的数学模型，用以帮助失联飞机的搜救者们规划一个有效的搜索方案。
失联飞机从A地飞往B地，可能坠毁在了大片水域（如大西洋、太平洋、印度洋、南印度洋、北冰洋）中。
假设被淹没的飞机无法发出信号。
你们的模型需要考虑到，有很多种不同型号的可选的飞机，并且有很多种搜救飞机，这些搜救飞机通常使用不同的电子设备和传感器。
此外，为航空公司撰写一份1-2页的文件，以便在其公布未来搜救进展的新闻发布会上发表。
2014美赛A题翻译问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。
大多数火车很长(也许10个或更多的汽车长)。
乘客走到出口的距离也很长，有整个火车区域。
每个火车车厢只有两个出口,一个靠近终端, 因此可以携带尽可能多的人。
每个火车车厢有一个中心过道和过道两边的座椅，一边每排有两个座椅，另一边每排有三个座椅。
走出这样一个典型车站,乘客必须先出火车车厢,然后走入楼梯再到下一个级别的出站口。
通常情况下这些列车都非常拥挤,有大量的火车上的乘客试图挤向楼梯，而楼梯可以容纳两列人退出。
大多数通勤列车站台有两个相邻的轨道平台。
在最坏的情况下,如果两个满载的列车同时到达,所有的乘客可能需要很长时间才能到达主站台。
建立一个数学模型来估计旅客退出这种复杂的状况到达出站口路上的时间。
假设一列火车有n个汽车那么长,每个汽车的长度为d。
站台的长度是p,每个楼梯间的楼梯数量是q。
美赛历年试题
2009 年美国大学生数学建模竞赛MCM、ICM 试题2009 MCM A: Designing a Traffic CircleMany cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.2009 MCM B: Energy and the Cell PhoneThis question involves the “energy” consequences of the cell phone revolution. Cell phone usage is mushrooming涌现, 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.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 householdhas a cell phone. Model the consequences of this change for electricity utilization使用 in the current US, both during the transition and during the steady state. The analysis should take into account the need for charging索价 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).Requirement 2Consider a second “Pseudo US”—a country of about 300 million people with about the same economic status as the current US. However, this emerging新兴的 country has neither landlines nor cell phones. What is the optimal最理想的 way of providing phone service to this country from an energy perspective观点? Of course, cell phones have many social consequences and uses that landline phones do not allow. A discussion of the broad明显的 and hidden隐藏的 consequences of having only landlines, only cell phones, or a mixture of the two is welcomed.Requirement 3Cell phones periodically定期的 need to be recharged.充电 However, many people always keep their recharger plugged 塞in. Additionally, many people charge their phones every night, whether they need to be recharged or not. Model the energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2.Assume that the Pseudo US supplies electricity from oil. Interpret 解释your results in terms of 就……而言barrels桶 of oil.Requirement 4Estimates vary on the amount of energy that is used by various recharger types (TV, DVR, computer peripherals, and so forth) when left plugged in but not charging the device.充电器插着单没用来给手机充电Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day.Requirement 5Now consider population and economic growth over the next 50 years. How might a typical Pseudo US grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements. Again, assume electricity is provided from oil. Interpret your predictions in term of barrels of oil.2008 年美国大学生数学建模竞赛MCM、ICM 试题2008 MCM A: Take a BathConsider the effects on land from the melting of the north polar ice cap due to the predicted increase in global temperatures. Specifically, model the effects on the coast of Florida every ten years for the next 50 years due to the melting,with particular attention given to large metropolitan areas. Propose appropriate responses to deal with this. A careful discussion of the data used is an important part of the answer.2008 MCM B: Creating Sudoku数独 PuzzlesDevelop an algorithm演算法 to construct 构造Sudoku puzzles 困惑of varying difficulty.Develop metrics公尺的 to define a difficulty level. The algorithm and metrics should be extensible 可扩充的to a varying number of difficulty levels.You should illustrate阐明 the algorithm with at least 4 difficulty levels.Your algorithm should guarantee a unique solution.Analyze the complexity复杂度 of your algorithm. Your objective目标 should be to minimize the complexity of the algorithm and meet the above requirements.2007 年美国大学生数学建模竞赛MCM、ICM 试题2007 MCM A: Gerrymandering选区不公正的重新划分Gerrymandering The United States Constitution宪法 provides that the House of Representatives shall be composed of 由什么组成some number (currently 435) of individuals who are elected from each state in proportion比例 to the state’s population relative相应的，成比例的 to that of the country as a whole. While this provides a way of determining how many representatives 州议员each state will have, it says nothing about how the district行政区，辖区 represented by a particular 特定的representative shall be determined geographically. This oversight疏忽出错 has led to egregious 极坏的(at least some people think so, usually not the incumbent) district shapes 情况that look “unnatural” by some standards. 标准Hence the following question: Suppose you were given the opportunity to draw congressional美国国会的 districts for a state. How would you do so as a purely纯粹的“baseline”基准线 exercise to create the “simplest” shapes for all the districts in a state?The rules include only that each district in the state must contain the same population. The definition of “simple” is up to you; but you need to make a convincing 令人信服的argument论据 to voters选举人 in the state that your solution is fair公平的. As an application应用 of your method, draw 草拟制定geographically地理上的 simple congressional districts for the state of New York.2007 MCM B: The Airplane Seating ProblemAirlines are free to seat passengers waiting to board上飞机 an aircraft in any order whatsoever无论什么. It has become customary习惯上的 to seat passengers with special needs first, followed by first-class 头等的passengers (who sit at the front of the plane). Then coach and business-class passengers are seated by groups of rows, beginning with the row at the back of the plane and proceeding行进 forward.Apart from consideration 考虑的事of the passengers’ wait time, from the airline’s point of view, time is money, and boarding time is best minimized. The plane makes money for the airline only when it is in motion,运转 and long boarding times limit the number of trips航行 that a plane can make in a day.The development of larger planes, such as the Airbus A380 (800 passengers), accentuate更突出 the problem of minimizing boarding (and deboarding) time.Devise想出 and compare procedures步骤 for boarding and deboarding planes with varying numbers of passengers: small (85–210), midsize (210–330), and large (450–800).Prepare an executive 执行的summary, not to exceed超出 two single-spaced pages, in which you set out your conclusions to an audience of airline executives, gate agents,代理人 and flight crews. 工作人员An article appeared in the NY Times Nov 14, 2006 addressing procedures currently当前 being followed and the importance to the airline of finding better solutions. The article can be seen at:/2006/11/14/business/14boarding.html2006 年美国大学生数学建模竞赛MCM、ICM 试题2006 MCM A: Positioning and Moving Sprinkler 洒水器Systems for Irrigation灌溉There are a wide variety of techniques available for irrigating a field. The technologies range from advanced drip洒下 systems to periodic 周期性的flooding. One of the systems that is used on smaller ranches is the use of “hand move” irrigation systems. Lightweight 轻量的aluminum 铝pipes 输送管with sprinkler洒水器 heads are put in place across fields, and they are moved by hand at periodic 周期性的intervals距离to insure that the whole field receives an adequate amount of water. This type of irrigation system is cheaper and easier to maintain 维修than other systems. It is also flexible, allowing for use on a wide variety of fields and crops. The disadvantage is that it requires a great deal of time and effort to move and set up the equipment at regular intervals. 距离Given that this type of irrigation system is to be used, h ow can it be configured 安装to minimize the amount of time required to irrigate a field that is 80 meters by 30 meters? F or this task you are asked to find an algorithm算法 to determine how to irrigate the rectangular矩形的field that minimizes the amount of time required by a rancher农场工人to maintain the irrigation system.One pipe输送管 set is used in the field. You should determine the number of sprinklers洒水器 and the spacingbetween sprinklers, and you should find a schedule计划表 to move the pipes, including where to move them.A pipe set consists of a number of pipes that can be connected together in a straight line. Each pipe has a 10 cm inner diameter直径 with rotating 转动spray喷雾器 nozzles 管嘴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厘米 of water every 4 days. The total amount of water should be applied as uniformly相同地 as possible.2006 MCM B: Wheel Chair Access at AirportsOne of the frustrations失败 with air travel is the need to fly through multiple多路的 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 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 护卫队to those people who ask for help. It is generally known well in advance which passengers require help, but it is not uncommon to receive notice when a passenger first registers 注册at the airport. In rare instances an airline may not receive notice from a passenger until just prior 在先前的to landing.Airlines are under constant pressure to keep their costs down. Wheel chairs wear out and are expensive and require maintenance.维修费 There is also a cost for making the escorts护卫队 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 severely 严重地limited in an airport terminal.总站 Also, wheel chairs left in high traffic areas represent a liability责任 risk as people try to move around 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 because it can affect the airline's average flight delay which can lead to fewer ticket sales as potential customers may choose to avoid an airline.Epsilon Airlines has decided to ask a third party to help them obtain a detailed详细的 analysis of the issues and costs of keeping and maintaining wheel chairs and escorts available for passengers. Theairline 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 索价to help them solve their problem. Your bid should include an overview 概要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 keep the total costs as low as possible. Your bid is one of many that the airline will consider. You must make a strong case 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 concourses), a medium (at least two concourses), and a small airport (one concourse) 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建议 to meet future needs.2005 年美国大学生数学建模竞赛MCM、ICM 试题2005 MCM A: Flood PlanningLake Murray in central South Carolina is formed by a large earthen dam, 水坝which was completed in 1930 for power production.Model the flooding downstream 顺流的，下游的in the event there is a catastrophic灾难的earthquake that breaches破坏 the dam.Two particular questions:Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver 下游的from the dam. How much flooding will occur in Rawls Creek from a dam failure,and how far back will it extend?Could the flood be so massive大规模的 downstream that water would reach up to the S.C. State Capitol Building, which is on a hill overlooking the Congaree River?2005 MCM B: Tollbooths收费站Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided 分开的highways that are interrupted at intervals距离 by toll通行费 plazas.广场 Because collecting tolls is usually unpopular, it is desirable 向往的to minimize 使减到最小motorist车主 annoyance恼怒 by limiting the amount of traffic disruption中断 caused by the toll plazas. Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza. Upon根据 entering the toll plaza, the flow of vehicles运载工具 fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze 压缩back down to a number of travel lanes equal to the number of travel lanes before the toll plaza. Consequently,结果 when traffic is heavy, congestion拥挤 increases upon departure离开 from the toll plaza. When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll.Make a model to help you determine the optimal最理想的 number of tollbooths to deploy使展开 in a barrier关口-toll plaza. Explicitly 明确地consider the scenario局面 where there is exactly one tollbooth per incoming travel lane.Under what conditions is this more or less effective than the current practice?Note that the definition of “optimal” is up to you to determine.2004 年美国大学生数学建模竞赛MCM、ICM 试题2004 MCM A: Are Fingerprints Unique?It is a commonplace belief that the thumbprint of every human who has ever lived is different. Develop and analyze a model that will allow you to assess the probability that this is true. Compare the odds (that you found in this problem) of misidentification by fingerprint evidence against the odds of misidentification by DNA evidence.2004 MCM B: A Faster QuickPass System“QuickPass” systems are increasingly appearing to reduce people's time waiting in line, whether it is at tollbooths, amusement parks, or elsewhere. Consider the design of a QuickPass system for an amusement park. The amusement park has experimented by offering QuickPasses for several popular rides as a test. The idea is that for certain popular rides you can go to a kiosk near that ride and insert your daily park entrance ticket, and out will come a slip that states that you can return to that ride at a specific time later. For example, you insert your daily park entrance ticket at 1:15 pm, and the QuickPass states that you can come back between 3:30 and 4:30 pm when you can use your slip to enter a second, and presumably much shorter, line that will get you to the ride faster. To prevent people from obtaining QuickPasses for several rides at once, the QuickPass machines allow you to have only one active QuickPass at a time. You have been hired as one of several competing consultants to improve the operation of QuickPass. Customers have been complaining about some anomalies in the test system. For example, customers observed that in one instance QuickPasses were being offered for a return time as long as 4 hours later. A short time later on the same ride, the QuickPasses were given for times only an hour or so later. In some instances, the lines for people with Quickpasses are nearly as long and slow as the regular lines.The problem then is to propose and test schemes for issuing QuickPasses in order to increase people's enjoyment of the amusement park. Part of the problem is to determine what criteria to use in evaluating alternative schemes. Include in your report a non-technical summary for amusement park executives who must choose between alternatives from competing consultants2003 年美国大学生数学建模竞赛MCM、ICM 试题2003 MCM A: The Stunt PersonAn exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.).Your job is to:∙determine what size boxes to use∙determine how many boxes to use∙determine how the boxes will be stacked∙determine if any modifications to the boxes would help∙generalize to different combined weights (stunt person & motorcycle) and different jump heightsNote that, in “Tomorrow Never Dies”, the James Bond character on a motorcycle jumps over a helicopter.2003 MCM B: Gamma Knife Treatment PlanningStereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators.The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical(approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a “shot.” Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most target volumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points.The goal of radiosurgery is to deplete tumor cells while preserving normal structures. Since there are physical limitations and biological uncertainties involved in this therapy process, a treatment plan needs to account for all those limitations and uncertainties. In general, an optimal treatment plan is designed to meet the following requirements.1.Minimize the dose gradient across the target volume.2.Match specified isodose contours to the target volumes.3.Match specified dose-volume constraints of the target and criticalorgan.4.Minimize the integral dose to the entire volume of normal tissuesor organs.5.Constrain dose to specified normal tissue points below tolerancedoses.6.Minimize the maximum dose to critical volumes.In gamma unit treatment planning, we have the following constraints:1.Prohibit shots from protruding outside the target.2.Prohibit shots from overlapping (to avoid hot spots).3.Cover the target volume with effective dosage as much as possible.But at least 90% of the target volume must be covered by shots.e as few shots as possible.Your tasks are to formulate the optimal treatment planning for a gamma knife unit as a sphere-packing problem, and propose an algorithm to find a solution. While designing your algorithm, you must keep in mind that your algorithm must be reasonably efficient.2002 年美国大学生数学建模竞赛MCM、ICM 试题2002 MCM A: Wind and WatersprayAn ornamental fountain in a large open plaza surrounded by buildings squirts 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 which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.2002 MCM B: Airline OverbookingYou're 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 dateBuild 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 company's 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 airline's CEO summarizing your findings and analysis2001 年美国大学生数学建模竞赛MCM、ICM 试题2001 MCM A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.∙Task 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel.The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments.(Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade.A rider will lose about 8 kph for a five percent grade over 100meters.∙Task 2. Provide an example of how the table could be used for a specific time trial course.∙Task 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way. Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web) by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data, if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:1.Under what conditions does the plan for turning the twocoastal-bound lanes of I-26 into two lanes of Columbia-boundtraffic, essentially turning the entire I-26 into one-way traffic, significantly improve evacuation traffic flow?2.In 1999, the simultaneous evacuation of the state's entire coastalregion was ordered. Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps。
翻译的美赛题目
PROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.Assume1. A width to length ratio of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced.Develop a model that can be used to select the best type of pan (shape) under the following conditions:1. Maximize number of pans that can fit in the oven (N)2. Maximize even distribution of heat (H) for the pan3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.问题A：终极布朗尼潘当在一个矩形的锅热烘烤时的4个角落中浓缩，并在拐角处（以及在较小程度上在边缘处）：产品会过头。
美赛赛题翻译
美赛赛题翻译
这次美赛有两份赛题，一份是“AI 生态圈的诊断和优化”，另一份是“基于 AI 的行业应用案例”。
“AI 生态圈的诊断和优化”
这次美赛要求选手对当前 AI 生态圈进行诊断，并提供有效的
优化方案，以促进AI 在中国的发展和落实。
选手需要从成本、创新力、知识产权、行业标准和企业间协作等多个方面，去分析和诊断当前 AI 生态圈，并针对这些方面提出实施、推动和
优化 AI 生态圈的政策和建议。
“基于 AI 的行业应用案例”
这次美赛要求选手提出习惯 AI 在不同行业的实践案例，可以
是经济体驱动的实用化行业案例，也可以是社会驱动的可持续性行业案例。
选手需要从大数据、机器学习、深度学习、人工智能等技术角度，准确识别案例所在行业的情况下，描述 AI
技术在有效解决问题、改善绩效和提升竞争力等方面发挥了什么作用，以及 AI 技术如何在案例中实施应用，并且从社会福祉、社会效益和社会影响等角度，阐述 AI 的价值与意义。
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2015年：A题一个国际性组织声称他们研发出了一种能够阻止埃博拉，并治愈隐性病毒携带者的新药。
建立一个实际、敏捷、有效的模型，不仅考虑到疾病的传播、药物的需求量、可能的给药措施、给药地点、疫苗或药物的生产速度，而且考虑你们队伍认为重要的、作为模型一部分的其他因素，用于优化埃博拉的根除，或至少缓解目前（治疗）的紧张压力。
除了竞赛需要的建模方案以外，为世界医学协会撰写一封1-2页的非技术性的发言稿，以便其公告使用。
B题回顾马航MH370失事事件。
建立一个通用的数学模型，用以帮助失联飞机的搜救者们规划一个有效的搜索方案。
失联飞机从A地飞往B地，可能坠毁在了大片水域（如大西洋、太平洋、印度洋、南印度洋、北冰洋）中。
假设被淹没的飞机无法发出信号。
你们的模型需要考虑到，有很多种不同型号的可选的飞机，并且有很多种搜救飞机，这些搜救飞机通常使用不同的电子设备和传感器。
此外，为航空公司撰写一份1-2页的文件，以便在其公布未来搜救进展的新闻发布会上发表。
2014美赛A题翻译问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。
大多数火车很长(也许10个或更多的汽车长)。
乘客走到出口的距离也很长，有整个火车区域。
每个火车车厢只有两个出口,一个靠近终端, 因此可以携带尽可能多的人。
每个火车车厢有一个中心过道和过道两边的座椅，一边每排有两个座椅，另一边每排有三个座椅。
走出这样一个典型车站,乘客必须先出火车车厢,然后走入楼梯再到下一个级别的出站口。
通常情况下这些列车都非常拥挤,有大量的火车上的乘客试图挤向楼梯，而楼梯可以容纳两列人退出。
大多数通勤列车站台有两个相邻的轨道平台。
在最坏的情况下,如果两个满载的列车同时到达,所有的乘客可能需要很长时间才能到达主站台。
建立一个数学模型来估计旅客退出这种复杂的状况到达出站口路上的时间。
假设一列火车有n个汽车那么长,每个汽车的长度为d。
站台的长度是p,每个楼梯间的楼梯数量是q。
使用您的模型具体来优化(减少)前往主站台的时间，有如下要求:要求1. 一个满载乘客的火车，所有乘客都要出火车。
所有乘客都要出楼梯抵达出主站台的路上。
要求2. 两个满载列车的乘客都要出车厢(所有乘客出到一个公用站台), 所有乘客都要出楼梯抵达出主站台的路上。
要求3.如果你能重新设计楼梯沿着站台的位置,那么这些楼梯应放置在哪,以缩短一列或两列火车的乘客出站所用的时间?要求4.乘客到达出主站台的路上所用的时间跟构建楼梯的台阶数有怎样的关系?要求5. 如果楼梯可以容纳K个人，那么时间会如何变化？k是大于1的整数除了要遵循HiMCM规范,准备一个简短的非技术物品向运输主管解释为什么他们应该采取你的模型来提高出站效率。
2014美国中学数学建模竞赛B题翻译问题二下一场瘟疫?在2014年，世界看到了感染埃博拉病毒在西非蔓延。
纵观人类历史，流行病来了又走，有些感染带到来然后杀死成千上万的人并且持续数百年，另外一些流行病导致少量的人员伤亡的。
一些人认为，这些事件只是大自然控制物种的生长方式，而其他人则认为，这可能是一个阴谋，或者是故意行为造成伤害。
这个问题很可能会归咎到如何花费（或不花费）稀缺资源（医生，防护设施，资金，科研，精华素等），以应对危机。
A部分：一个常见的人道主义报道：在印度尼西亚的一个岛上的一个小村庄，那里的300名居民中几乎有一半都出现了类似的症状。
在过去的一周，15个“传染”着已经死亡。
这个村与附近的村庄和其他岛屿进行交易而出名。
您的建模团队工作的疾病控制的一个主要中心是在贵国的首都（或者，如果你喜欢，可以说是国际世界卫生组织）。
要求1：建立一个数学模型执行以下功能，包括如何/何时最佳分配这些稀缺资源...- 确定和分类的疾病传播的类型和严重程度- 或者，确定疫情是否受控（爆发）- 引发适当的措施（什么时候治疗，什么时候运送受害者，什么时候限制转移，什么时候让疾病听其自然，等等）去控制某种疾病。
注意：此时你可能要开始使用著名的“SIR”模型或该模型的部分，或者考虑别的修正后的SIR模型，多个模型，或者创建自己的模型。
要求2：根据所给出的信息、你的模型以及你的团队所做的假设，你的团队需要为你的国家疾病预防控制中心给出哪些初步建议？（3-5给出建议，理由）附加态势信息：多国研究小组花7天聚集在村里被感染后的信息返回给你的国家首都。
要求3：你可以要求问他们3个问题，以改进你的模型。
你需要问什么问题和原因？附加情境信息：多国研究小组得出结论一致认为，本病：-出现传播是通过与受感染者的体液接触-如果感染，老人和儿童更容易感染-附近的岛上开始出现类似感染的迹象-一个研究者返回到贵国首都出现感染要求4：如何根据以上的附加信息改版/修改模型？要求5：写下你的发现，为当地的非技术广播电台(或电视台)提供新闻稿。
2013年PROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.Develop a model to show the distribution of heat across the outer edge of a panfor pans of different shapes - rectangular to circular and other shapes in between.Assume1. A width to length ratio of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced.Develop a model that can be used to select the best type of pan (shape) under the following conditions:1. Maximize number of pans that can fit in the oven (N)2. Maximize even distribution of heat (H) for the pan3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.（译文：A:当在一个矩形的锅中烘烤时热量集中在锅的4个角落中，并在角落处的食物烤的过了（在某种程度上边缘也是这样）。
在一个圆形盘的热量被均匀地分布在整个外缘，在边缘处的食物烤的不会过头。
然而，因为大多数烤箱是方形的，使用原型的平底锅效率是不高的相对于烤箱中的空间。
建立一个模型来说明不同形状的锅(圆形方形或其他形状)的外边缘热量的不同分布。
假设:1.矩形烤箱的的宽度与长度之比是W / L。
2.每个盘子的面积都是A3.最初，两个机架在烤箱，间隔均匀。
建立一个模型，在下列情况下，可用于选择最佳的锅（形状）：1.可以放到烤箱中的锅的最大数量是（N）2.烤箱里最大限度地均匀分布热量为（H），3.优化的组合的条件（1）和（2）式的权重p和(1 – p)，用来说明如何随不同的值的W/L和P的变化而影响最终结果。
除了你的格式化的解决方案,准备一个一到两页的广告页为新布朗尼美食杂志突出自己的设计和结果。
）PROBLEM B: Water, Water, EverywhereFresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, and cost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outliningyour approach, its feasibility and costs, and why it is the “best water strategy choice.”Countries: United States, China, Russia, Egypt, or Saudi Arabia（问题B:水,水,到处都是淡水已经是约束世界上大部分国家发展的一个限制条件。