2013美国数学建模题目以及部分翻译

2013 Contest Problems

MCM PROBLEMS

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).矩形的平锅

In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. 圆形锅，热量均匀地分布在所有的边缘

However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.大多数的灶是矩形的，用圆锅没有效率

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.建立模型，展示不同形状的锅子外部边缘上热量的分布，

Assume

1. A width to length ratio of W/L for the oven which is rectangular in shape. 炉灶的长宽比是矩形

2. Each pan must have an area of A.

每个平锅面积都是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)

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