2013年美国数模A试题及翻译.doc

2013 美赛资源共享 2013 Contest ProblemsMCM PROBLEMS我也在参加美赛啊、资料共享 www_coolwb_comPROBLEM 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.当在一个矩形的锅热烘烤时热量几种在烤箱的4个角落中，并在角落处的食物烤的过了（在某种程度上边缘也是这样）。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实物烤的不会过头。然而，因为大多数烤炉使用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。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.建立一个模型来说明不同形状的锅(圆形方形或其他形状)的外边缘热量的不同分布。Assume1. A width to length ratio ofW/Lfor the oven which is rectangular in shape.2. Each pan must have an area ofA.3. Initially two racks in the oven, evenly spaced.假设1. 矩形烤箱的的宽度与长度之比是W / L。2. 每个盘子的面积都是A3. 最初，两个机架在烤箱，间隔均匀。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 pan3. 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 ofW/Landp.建立一个模型，可用于选择最佳的盘子（形状）在下列情况下：1. 可以放到烤箱中的锅的最大数量是（N）、2. 盘子里最大限度地均匀分布热量为（H），3. 优化的组合的条件（1）和（2）式中的权重p和(1 p)，用来说明如何随不同的值的W/L和P的变化而影响最终结果。In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazi