2013数学建模美赛题目(中文版)

介绍今年的焦点问题是如何实现质量和数量的平衡。

在质量方面，尽可能使热量均匀地分布。

目标是降低或避免矩形烤盘四个边角发生热量聚集的情况。

所以解决热量均匀分布这方面的问题，使用圆形烤盘是最佳的选择。

在数量方面，应该使烤盘充分的占据烤箱的空间。

所以我们的目的是使用尽可能多的烤盘来充分占据烤箱的空间，此时矩形烤盘是最佳选择。

对于这方面的问题的解决，就要考虑烤盘在烤箱水平截面上所占的比率。

在这个评论中，我们首先描述判断步骤，然后再讨论队伍对于三个问题的求解。

下一个话题就是论文的灵敏度和假设，紧随其后讨论确定一个给定方法的优势和劣势。

最后，我们简短的讨论一下参考和引用之间的区别。

过程第一轮的判别被称为“分流轮”。

这些初始轮的主要思想是确定论文应被给予更详细的考虑。

每篇论文应该至少阅读两次。

在阅读一篇论文的时候，评审的主要问题是论文是否包含所有必要的成分,使它成为一个候选人最详细的阅读。

在这些初始轮中，评审的时间是有限制的，所以我们要尽量让每一篇论文得到一个好的评判。

如果一篇论文解决了所有的问题，就会让评审觉得你的模型建立是合理的。

然后评审可能会认为你的论文是值得注意的。

有些论文在初轮评审中可能会得到不太理想的评论。

特别值得注意的是，一篇好的摘要应该要对问题进行简要概述，另外，论文的概述和方法，队员之间应该互相讨论，并且具体的结果应该在某种程度上被阐述或者表达出来。

在早期的几轮中，一些小细节能够有突出的表现，包括目录，它更便于评委看论文，同时在看论文的时候可能会有更高的期待。

问题求解也很重要。

最后，方法和结果要清晰简明的表达是至关重要的。

另外，在每个部分的开始，应该对那个部分进行一个概述。

在竞赛中，建模的过程是很重要的，同时也包括结论的表达。

如果结果没有确切和充分的表达，那么再好的模型和再大努力也是没有用的。

最后的回合最后一轮阅读的第一轮开始于评委会会议。

在这个会议中，评委将进行讨论，他们会分享他们各自认为的问题的关键方面。

2013 竞赛题目
MCM
问题A：
当在矩形平底锅上烘烤食物时，热量集中在四个角，因此食物在四个角上容易烤焦（边上焦的程度较轻一点）。

在圆形平底锅内烘烤时，热量均与地分布于整个外部边缘，食物的边缘部分不会烤焦。

然而，由于大部分烤炉形状为矩形，就利用烤炉中的空间而言，使用圆形平底锅并不是最有效率的做法。

开发一个模型来展现平底锅外边缘热量分布，该平底锅的形状可为矩形或圆形，也可能是其它形状。

假设
1．矩形烤炉长宽比W/L
2．每个平底锅面积为A
3．初始烤炉中的两个架子在空间上平均分布。

开发一模型可用于在下列条件下挑选最佳类型的平底锅（形状）：
1．最大限度提高放入烤炉中的平底锅数量（N）
2．最大限度均匀分布在平底锅上的热量分布（H）
3．最优组合条件（1）和（2），其中指定权值p和（1-p）来解释这些结果如何随W/L和p 的不同值变动。

除了MCM格式化的解决方案，为新的《布朗尼美食家杂志》准备一至两页的广告，表达你的思路。

问题B：水，水，到处都是水
新鲜的水对于世界各地的发展是一个限制性因素。

建立一个数学模型用于决定一个有效、可行且成本效益最大的2013水战略来应对投射出来的2025年水需求[从下列国家中挑选一个国家]，并确认最佳水资源战略。

尤其要注意的是，你的模型必须强调存储量和水的运动；去盐渍及保水。

如果可能的话，使用你的模型来讨论你拟定战略的经济、物理和环境影响。

向政府官员提供一个非技术性意见书，阐述你的方法、可行性和成本，以及你的战略之所以为“最佳水资源战略选择”的原因。

国家：美国，中国，俄国，埃及或沙特阿拉伯。

Problem c:背景：社会正致力于运用和开发模型来预测地球的生物和环境情况。

很多科学研究总结了逐渐增长的地球环境和生物系统压力，但很少有人用全球范围的模型来检测这些观点。

联合国发表的千年生态系统评估综合报告发现：近三分之二的地球生命支持生态系统——包括净水，洁净的空气，稳定的气候——正在因非可持续性使用而逐渐衰减。

其中大部分破坏归咎于人类行为。

暴增的对于食物，淡水，燃料，木材的需求导致了剧烈的环境变化；从森林砍伐到空气，土壤和水污染。

尽管已存在大量关于局部习惯和地区因素的研究，目前的模型还不能告知决定人他们的局部策略是如何影响整个地球的健康的。

许多模型忽略了复杂的全球因素，这些模型无法判断重大政策的长期影响。

尽管科学家们意识到巨大环境和生物系统中存在的复杂关系和交叉作用，当前的模型通常忽略这些管理或限定了系统间的影响。

系统的复杂性体现在多元交互（多个元素的相关性），反馈，突发行为，即将发生的状态变化或触发点。

最近的自然杂志中一篇由22位国际知名科学家撰写的题为“迫近地球生物圈的状态变化”的文章讨论了许多有关科学模型对于预测行星健康系统潜在状态变化的重要性与必需性。

文章提供了两种具体定性的模型，并寻求更好的预测模型：1）通过在全球模型中加入相关系统的复杂性（包括局部情况对全球系统的影响，反之亦然）来优化生物状态预测。

2）辨别不同因素在产生非健康全球状态变化中的作用并展示如何运用有效的生态系统管理来预防或限制这些即将发生的状态变化。

研究最终归结于问题：我们是否能利用全球健康的局部或地区性组成部分预测潜在状态变化来帮助决策者制定基于对全球健康状况潜在影响的，有效的策略。

尽管有越来越多的警示信号出现，没人知道地球是否确实在接近全球性的转折点（极端状态），这种极端的状态是否是不可避免的。

自然杂志等研究指出了地球生态系统中的一些重要工作元素。

（例如：局部因素，全球变化，多维元素与关系，变化的时间与空间范围）。

2013 Contest ProblemsMCM 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。

现在需要他们的解决方案文件太solutions@为Word或PDF附件的电子邮件提交电子副本（汇总表和解决方案）队（由学生或者指导教师）。

COMAP的提交截止日期为2013年2月4日美国东部时间下午8:00，必须在收到您的电子邮件。

主题行COMAP是你的控制示例：COMAP 11111点击这里下载PDF格式的完整的竞赛说明。

点击这里下载Microsoft Word中的格式汇总表的副本。

*请务必变更控制之前选择打印出来的页面的数量和问题。

团队可以自由选择之间MCM问题MCM问题A，B或ICM问题C.COMAP镜像站点：更多：/undergraduate/contests/mcm/MCM：数学建模竞赛ICM：交叉学科建模竞赛2013年赛题MCM问题问题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。

在一个圆形盘的热量被均匀地分布在整个外缘和在边缘处的产品不过头。

然而，因为大多数烤炉使用圆形平底锅的形状是矩形的是效率不高的相对于使用在烘箱中的空间。

开发一个模型来显示横跨平底锅平底锅不同形状 - 矩形之间的圆形和其他形状的外边缘的热量分布。

假设1。

的宽度与长度之比的W / L的形状是矩形的烘箱。

2。

- 每个盘必须具有的区域A的3。

最初，两个机架在烤箱，间隔均匀。

建立一个模型，可用于选择最佳的泛类型（形状）在下列情况下：1。

适合在烤箱的锅，可以最大限度地提高数（N）2。

最大限度地均匀分布热量（H），泛3。

优化的组合的条件（1）和（2）式中的权重p和（为1 - p）被分配的结果来说明如何随不同的值的W / L和p。

在除了MCM格式解决方案中，准备一到两页的广告片的新布朗尼美食杂志突出自己的设计和结果。

问题B：水，水，无处不在新鲜的白开水是在世界大部分地区的发展限制约束。

建立一个数学模型，为确定有效的，可行的和具有成本效益的水资源战略于2013年，以满足预计的用水需求，从下面的列表]中选择一个国家，到2025年，确定最佳的水战略。

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 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.当在矩形盘子中烘烤食物时，热量会集中于四个角。

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.当用一个矩形的平底锅烘焙时，热量集中在锅的四个角，因此蛋糕在四个角落及其附近会烤过头。

2013 Contest Problems
MCM PROBLEMS
今天美赛成绩也出来了，想起去年年前在学校准备竞赛的苦日子，心里也算有了一丝丝的安慰。

这是去年竞赛时候学校请的两位美女外援英语老师帮忙做的题目翻译。

贡献出来了，呵呵，不能埋没了她们的才华。

——francis_hao
A题：
用矩形的烤盘烤东西，盘子四角加热不均，容
用圆形盘子烤东西，热量分配均匀，食物的边缘不容易被烤焦。

但是，大多数的烤箱都是矩形的，使用圆形的盘子没有将烤箱的空间充分的利用
建模型：分别说明矩形、圆形和其他介于两者之间形状的盘子在热量分布上的区别
假设：
1.烤箱的长宽比是W/L
2.盘子的面积是A
3.烤箱中的两个架子是平均分布的。

建模型：按照以下条件，选择最优形状
1、在满足烤箱大小的限度下使盘子数量N最大化
2、使盘子均匀受热最大化
3、将1和2结合，说明W/L以及p的变化对结果有什么影响
B题
淡水资源对于世界上大多国家都是限制性的资源。

建一个数学模型确定2013年一个有效、可行、成本低的水利战略，满足2025年的水需求，并制定最好的水利战略（国家如下表）。

数学模型必须能存储、运输、去盐碱化和利于保存。

如果可能，你的模型会讨论水利战略关于经济、物理上以及对环境的后果。

给政府领导提供一个非技术性论文概括你的方法，包括可行性、花销以及此方法是最优水利战略的原因。

国家：美国、中国、俄罗斯、埃及、沙特阿拉伯。

2013年数学建模题目
以下是2013年数学建模竞赛题目：
A题：最佳巧克力蛋糕烤盘
题目要求建立一个模型，描述在不同形状烤盘表面热量的分布情况，以及每个烤盘的面积A。

B题：水，水，无处不在
题目要求建立一个数学模型，来确定满足某国未来用水需求的有效的、可行的、低成本的2013年用水计划，并确定最优的淡水分配计划。

模型必须包括储存、运输、淡化和节水等环节。

C题：地球健康的网络建模
题目要求研究与应用模型来预测地球的生物和环境的健康状况。

D题：变循环发动机部件法建模及优化
题目涉及到变循环发动机的基本构造、工作原理、两种工作模式（涡喷模式和涡扇模式），以及变循环发动机部件建模法的燃气涡轮发动机的特性（可以用实验方法和计算方法获得）。

2013 Contest ProblemsMCM PROBLEMSPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corner s and the product gets overcooked at the corners (and to a lesser ext ent 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 edg e 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 i n 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 a nd (1- p) are assigned to illustrate how the results vary with differ ent 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.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, feas ible, and cost-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 mo del must address storage and movement; de-salinization; and conservat ion. If possible, use your model to discuss the economic, physical, a nd environmental implications of your strategy. Provide a non-technic al position paper to governmental leadership outlining your approach, its feasibility and costs, and why it is the “best water strategy c hoice.”Countries: United States, China, Russia, Egypt, or Saudi Arabia 2013 Contest ProblemsMCM PROBLEMSPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corner s and the product gets overcooked at the corners (and to a lesser ext ent 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 edg e 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 i n 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 a nd (1- p) are assigned to illustrate how the results vary with differ ent 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.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, feas ible, and cost-efficient water strategy for 2013 to meet the projecte d water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical mo del must address storage and movement; de-salinization; and conservat ion. If possible, use your model to discuss the economic, physical, a nd environmental implications of your strategy. Provide a non-technic al position paper to governmental leadership outlining your approach, its feasibility and costs, and why it is the “best water strategy c hoice.”Countries: United States, China, Russia, Egypt, or Saudi Arabia。

2013 ICM ProblemNetwork Modeling of Earth's HealthBackground: Society is interested in developing and using models to forecast the biological and environmental health conditions of our planet. Many scientific studies have concluded that there is growing stress on Earth's environmental and biological systems, but there are very few global models to test those claims. The UN-backed Millennium Ecosystem Assessment Synthesis Report found that nearly two-thirds of Earth's life-supporting ecosystems— including clean water, pure air, and stable climate— are being degraded by unsustainable use. Humans are blamed for much of this damage. Soaring demands for food, fresh water, fuel, and timber have contributed to dramatic environmental changes; from deforestation to air, land, and water pollution. Despite the considerable research being conducted on local habitats and regional factors, current models do not adequately inform decision makers how their provincial polices may impact the overall health of the planet. Many models ignore complex global factors and are unable to determine the long-range impacts of potential policies. While scientists realize that the complex relationships and cross-effects in myriad environmental and biological systems impact Earth's biosphere, current models often ignore these relationships or limit the systems' connections. The system complexities manifest in multiple interactions, feedback loops, emergent behaviors, and impending state changes or tipping points. The recent Nature article written by 22 internationally known scientists entitled "Approaching a state shift in Earth's biosphere" outlines many of the issues associated with the need for scientific models and the importance of predicting potential state changes of the planetary health systems. The article provides two 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 impending state 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's health (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. Be sure 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 your model and explain where human behavior and government policies could affect the results of your model.Requirement 2: Run your model to see how it predicts future Earth health. You may need 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 it for 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 inform decision makers on important policies? Do you take into account the human elements in your measures and network properties?Requirement 3: One of the powerful elements of using network modeling is the ability to 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 model to missing links or changing relationships? Does your model use feedback loops or take into account uncertainties? What are the data collection issues? Does your model 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 20 pages) 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.。

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。

2013 Contest ProblemsMCM 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.终极蛋糕烤箱当用矩形烤盘烘焙时，热量集中在4个角落，在角落的食物容易被烤糊（边上的热量较少），在一个圆形烤盘上，热量均匀的分布在盘的整个边缘，而且分布在边缘的食物不会被过度加热。

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.Problem A: 终极布朗尼锅当在一个矩形的锅里烹煮食物时，受热集中在锅的4个角落里，因此食品在这4个拐角处被过度烹饪（在边缘程度会稍微轻点）。

2013年美国大学生数学建模和跨学科建模竞赛试题
叶其孝
【期刊名称】《数学建模及其应用》
【年(卷),期】2013(002)002
【摘要】A题:最佳果仁巧克力食品烤盘在矩形烤盘中烘烤食品(例如蛋糕)时热量集中在4个角点处,而食品也在这些角点处烤过头(在4条边处不那么过头)。

在圆形烤盘中沿其外边缘热量均匀分布,食品不会在外边缘烤过头。

然而,因为大多数烤箱是矩形的,所以就利用烤箱的空间而言使用圆形烤盘效率不高。

研制(数学)模型来展示不同形状烤盘——矩形、圆形以及介乎其间的各种形状的烤盘——在穿过其外边缘时的热量分布。

假设:1.矩形烤箱的宽长比为W/L;2.每种烤盘的面积必须为A;3.两个搁物网架均匀放置在烤箱中。

研制能够在下列条件下选择最佳烤盘形状的(数学)模型:(1)使烤箱中能容纳的烤盘数最大(N);
【总页数】3页(P50-52)
【作者】叶其孝
【作者单位】
【正文语种】中文
【相关文献】
1.2015年美国大学生数学建模和跨学科建模竞赛试题(A题和B题) [J], 周蓉;
2.2014年美国大学生数学建模和跨学科建模竞赛试题 [J], 王艳慧
3.2014年美国大学生数学建模和跨学科建模竞赛试题 [J], 王艳慧;
4.2013年美国大学生数学建模和跨学科建模竞赛试题 [J], 叶其孝;
5.2012年美国大学生数学建模和跨学科建模竞赛试题 [J], 叶其孝
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数学和经济灾难2008年的市场崩溃,世界陷入经济衰退,仍是有许多原因。

其中一个是数学。

金融世界并不孤独,当然,在根据数学模型并不总是可靠的决策指导。

科学家与模型在许多fields-including （包含领域）气候科学,海岸侵蚀和核safety-in（安全植入）他们描述的现象是非常复杂的,或信息很难获得,或者,与金融模型一样,两者皆有。

这些公式或模型,只是苍白的反映现实世界,有时他们会严重误导。

尽管他们无处不在,这些风险模型未能考虑影响市场的重要力量。

研究人员正在构建方法来绕过这些限制和防止重复市场崩盘。

然而,这些策略可能会限制利润,因此,银行不太可能采纳没有被迫这样做如果可能的话,你可以重新定义风险,然后构建一个动态模型的一些主要因素的市场监控触发或症状减少潜在的意外经济灾难归咎于风险模型将是一个过于简单化。

其他人类factors-political（政治因素）和监管ones-certainly （人员确定）发挥作用。

如何减少人类的影响?除了比赛的格式,准备一个1 - 2页非技术信金融投资公司的最终建议我自己的理解和翻译：2008年国际金融市场遭受了很大的冲击，这是由很多因素造成的，其中一个就是数学。

当然，金融世界并不是完全独立的，他取决于数学模型，而这个数学模型并不是完全依赖于设定的市场规则。

科学家在很多领域尝试数学模型，他包括:气候科学，海岸侵蚀，核安全；在这些问题中它描述的非常复杂，而且信息很难被获取，而这些和金融模型是一样的。

这些方案或模型，只是苍白无力反应真实世界，有的甚至可怜的是个错误结果。

尽管这些问题普遍存在，这些激进的模型在考虑重要力量影响市场时仍然失败了，研究者建立新的方法来解决他们的限制和防止重复的市场冲击。

这些策略可能限制利润，而且不可能使银行适应他们没有按照强迫被要求去做的事。

1.如果可能的话，你可以重新定义风险，然后建立一个动态模型市场的主要因素监控触发器或症状减少潜在的意外。

2013 Contest ProblemsMCM 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, and cost-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 andmovement; 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 Arabia。