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1、PROBLEM A: The Ultimate Brownie Pan 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
2、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 bet
3、ween.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 p
4、ans 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
5、 a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results. 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
6、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。PROBLEM B: Water, Water, EverywhereFresh water is the limiting
7、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
8、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 feas
9、ibility 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，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。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，物理和环境的影响，你的战略。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，沙特阿拉伯西南交-成型(1003810659) 20:00:56有没准确点的翻译的
