人教版小学数学一年级2013数学建模题目

2020年11月19日发(作者：殷契)

PROBLEM A: The Ultimate Brownie Pan最终的布朗尼锅

When 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.
烘烤时，在一个长方形的锅热集中在4角和产品得到了在角落（以及在较小程度上的 边缘
处）。在一个圆形锅热均匀分布在整个外边缘和产品不烂的边缘。然而，由于大多数炉在使
用圆形锅是矩形形状不是有效的在一个炉使用的空间。

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.
发展一个模型在不同形状的- 之间的循环和其他形状的矩形平底锅锅外边缘的热分布。

Assume
1. 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.
假设

1。该炉，形状为矩形的W / L的长度比宽度。

2。每盘必须有一个面积

3。最初的两个架在炉中，均匀间隔的。

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 pan
3. 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.
开发了一个可以用来选择最好的模型锅（形状）在下列条件：

1。锅炉号，可以最大化（N）

2。最大限度地提高热分布均匀（H）为潘

3。优化的条件的组合（1）和（2），P和权重（1 - P）被分配来说明结果随W／L和P值不
同

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.
除了你的MCM格式化的溶液，准备一一为新的布朗尼美食杂志突出你的设计和结 果两页的
广告片。



PROBLEM B: Water, Water, Everywhere水，水，到处都是

Fresh 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 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.”
新鲜的水是在世 界的许多地方发展的限制因素。建立了用于确定一个有效的，可行的数学模
型，和成本有效的水战略20 13满足未来的用水需求，[ 2025 ]从下面的列表中选择一个国家，
并确定水的最佳策略。特别 是，你的数学模型必须解决存储和移动的盐渍化；保护。如果可
能的话，使用你的模型，讨论经济，物理 ，和你的战略环境的影响。提供一个非技术性职位
介绍政府领导概述你的方法，其可行性和成本，以及为 什么它是“最好的水战略的选择。”

Countries: United States, China, Russia, Egypt, or Saudi Arabia
美国，中国，俄罗斯，埃及，沙特阿拉伯


Network Modeling of Earth's Health
地球的健康网络建模

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
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:
社会是有兴趣在开发和使用模型来预测

生物和环境对我们星球的健康状况。许多科学研究

得出的结论是，有越来越多的应力对地球环境和生物

系统，但也有极少数的全球模型来检验这些主张。联合国支持的

千年生态系统评估综合报告发现，近三分之二的

地球上的生命支持系统包括干净的水，纯净的空气，和稳定

气候是由不可持续的利用退化。人类在很大程度上导致了

这种损伤。飞涨的粮食需求，新鲜的水，燃料，以及木材的贡献



剧烈的环境变化；森林砍伐和土地，空气，水污染。

尽管相当多的研究在当地的栖息地和区域进行

因素，目前的模型没有充分告知决策者如何省

政策可能会影响地球的整体健康。许多模型都忽略了复杂的全球

因素，无法确定潜在的政策的长期影响。什么时候

科学家认为，复杂的关系和无数的交叉影响

环境和生态系统的影响地球的生物圈，电流模型往往

忽略这些关系或限制系统的连接。该系统的复杂性

体现在多元互动，反馈回路，应急行为，临

状态的变化或临界点。最近的自然条22国际书面

著名的科学家为“接近状态改变了地球生物圈”概述了许多

相关的问题的科学模型的必要性和重要性的

预测行星健康系统的潜在状态的变化。本文提供了

两个具体的量化建模的挑战，他们要求更好的预测模型：
1) To improve bio-forecasting through global models that embrace the
complexity
of Earth's interrelated systems and include the effects of local conditions on
the
global system and vice versa.
2) To identify factors that could produce unhealthy global state-shifts and to
show
how to use effective ecosystem management to prevent or limit these
impending
state changes.
1）提高通过全球模型，拥抱的复杂性预测生物

地球的相互关联的系统，包括当地条件的影响

全球系统和反之亦然。

2）确定的因素，可能产生不健康的全局状态的变化和显示

如何利用有效的生态系统管理，防止或限制这些即将到来的

状态的变化。

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.
所研究的问题是我们是否可以使用本地或全球模型的建立

区域组成的地球的健康，预测潜在的状态变化和帮助

决策者设计的基础上，对地球的潜在影响，有效的政策

健康。虽然许多警告标志的出现，没有人知道地球是

真正接近全球引爆点或者如果这种极端的状态是不可避免的。

自然杂志文章和其他许多人指出，有几个重要的元素

在地球的生态系统（例如，局部因素，全球影响，多维

因素和关系，不同时间和空间尺度）。还有许多其他的

这可以包括在预测模型- 人口因素，资源

栖息地的应力，生境改造，能源，气候变化，土地利用

模式，污染，大气化学，海洋化学，生物多样性，政治

图案如社会动荡和经济不稳定。古生物学家的研究

和模拟生态系统的行为和反应在以前的激变状态的变化

因此，历史为基础的定性和定量的信息可以提供背景

对未来的预测模型。然而，应该指出的是，人类的影响

在我国目前的生物圈的情况显著增加。
Requirements:
You are members of the International Coalition of Modelers (ICM) which will soon be
hosting a workshop entitled
leader has asked you to perform modeling and analysis in advance of the workshop.
He requires your team to do the following:
要求：

你是建模者的国际联盟的成员（ICM）将很快

举办了一个题为“网络与健康”地球和你的研究

领导要求你在车间提前进行建模和分析。