2013美国数学建模题目1.2翻译.doc

2013 Contest Problems MCM PROBLEMS PROBLEM A: The Ultimate Brownie Pan 最后的布朗尼平底锅当我们用矩形平底锅烹饪时，热量会集中在4个角落并且角落被烹饪的东西会被过分加热（同时在边缘烹饪效果会减弱）；当是一个圆形锅时热量会被等量分布在整个外边缘并且边缘的食物不会被过分加热。但是，因为目前大多数烤炉是矩形的所以用圆形的烤盘在空间的利用上效率不好。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.建立一个对于不同形状烤盘外延热量分布的模型-矩形圆形两者之间的形状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.假设：1.矩形烤箱宽与长的比例为 W/L2.每个烤盘的面积为A3.最开始每个烤箱有两个烤架，平均放置在下面所提的条件下建立数学模型来选择烤盘的最佳形状1.使尽可能多的烤盘可以放在烤炉中2.使烤盘平均分配的热量尽量大3.优化条件1和条件2的组合情况，利用权重P和和（1-P）来说明随着不同宽长比W/L和重量P的变化时结果的变化情况。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. 除了准备你对于MCM美赛的书面解答外，为BG这个杂志准备一个12页的广告介绍材料来彰显出你的设计和结果的优秀和与众不同。PROBLEM B: Water, Water, Everywhere，到处都是水啊！在世界上的大多数地方，淡水一直是限制发展的重要阻碍和约束。建立数学模型来确定一个有效（效果显著），可行性好的，并且花费合理经济的用水策略来满足X国（从下面的列表中随机选择一个国家）2025年的计划用水需求，并且确定最佳的用水政策策略。要注意的是，你的模型必须注明水的容量和流动情况（流量），海水淡化的情况和相应的保护保存的情况。尽可能去使你的模型把你策略中的经济性，自然性物理性，和环境等情况也考虑进去。为政府的领导层提供一份非技术性的意见书，并且要想办法使你的方法脱颖而出，包括他的可行性，花费情况并解释为什么您的方法是最好的水使用策略的选择。国家：美国，中国，俄罗斯，埃及，沙特阿拉伯。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.” Countries: United States, China, Russia, Egypt, or Saudi Arabia ICM PROBLEMPROBLEM C: Network Modeling of Earths Health 地球健康的网络模型Click the title below to download a PDF of the 2013 ICM Problem.Your ICM submission should