2013年美国数学建模竞赛试题.doc

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 overthe 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 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. In addition to your MCM formatted solution, prepare a one to two pageadvertising 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 theworld. 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 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 overthe 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 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. In addition to your MCM formatted solution, prepare a one to two pageadvertising 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 theworld. 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 MCMA 题当在一个方形平底锅烘烤时，由于热量集中在四个角上，在角上的（和在伸展度小的边缘）食物就会过度烹饪，圆形平底锅热量平均分配在整个外缘，在边上的食物不会过度烹饪。

然而，由于大部分烤箱都是方形，考虑到烤箱空间的使用，圆形锅不会有效的利用烤箱的空间目的：建立一个模型对于不同形状锅的边缘的热量分布，方形到圆形或他们中任一形状假设方形烤箱的宽长比是 W/L每个锅都有一个 A 型区域首先，烤箱有两个烤架，并且均匀分布在如下条件下建立一个模型，用来选择在形状上最好类型的锅可以放在烤箱里的最大化数量的锅能最大化均匀分布热的锅优化组合的条件 1 和 2，重量 P 和（1-P）被分配来说明结果怎样随 W/L 和 P 的值变化而变化问题 B：水，水，无处不在新鲜水是对世界大部分地区的发展限制约束建立一个数学模型，为 2013 年确定有效的，可行的和具有成本效益的水资源战略，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，确定最佳的水资源战略特别是，您的数学模型必须解决存储和运动，去盐碱化和保护如果可能的话，用你的模型，探讨经济，物理和环境对你的战略影响提供一个非技术性的立场文件，政府领导介绍你的方法，其可行性和成本，以及为什么它是“最好的的水战略选择 ”国家有：美国，中国，俄罗斯，埃及，沙特阿拉伯。