2013年美赛A中文翻译(标准版).doc

精品文档问题A： 终极布朗妮平锅当用长方形平底锅炒菜时，热集中于四个角，因此四个角的食物就炒糊了（四个边上的食物炒糊的程度略微轻一点）。用圆形平底锅时，热会均匀地分布在整个外部边缘，因此锅边的食物就不会炒得太过。然而，大多数炉子在形状上都是长方形的，那么考虑到炉子的空间使用，用圆形平底锅就不是很经济。建立一个模型来说明热在不同形状的平底锅外部边缘的分布长方形平底锅，圆形平底锅或介于两都者之间的其他形状的平底锅。假设：1. 长方形炉子的宽长比为W/L。2. 每个平底锅必须有一个面积A。3. 最初的时候，炉子里两个层架的空间是均匀的。建立一个模型，基于以下条件，用以选择最好的平底锅（形状）：1. 使适合炉子的平底锅的数量最大化（N）。2. 使平底锅上热（H）的平均分布最大化。3. 优化条件（1）和（2）的组合，条件（1）和（2）的权重P和（1P）是用来表示结果是如何随着W/L 和 p的取值变化而变化的。除了根据MCM格式要求的解决方案外，你还需为新一期的“布朗妮美食杂志”准备一到两页的广告页来突出你的设计和结果。Hewlett-PackardHP LaserJet 1018PROBLEM 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 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 page ad