2013MCM数学建模美赛A题中英文对照

PROBLEM A: The Ultimate Brownie Pan

问题A：终极布朗尼蛋糕盘

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).

当蛋糕在矩形盘里加热时，热量会集中在蛋糕的四个角导致加热过度（在较小的边缘处也有这种情况）。 In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges.

在圆形的盘子里，热量均匀的分布在蛋糕表面，所以不会加热过度。

However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.

然而，由于大多数的烤箱是矩形的，使用的盘子是圆形的，不能有效的利用烤箱里的空间。

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.

建立模型来显示在使用不同形状的盘子时（方形，圆形和两者之间的其他形状），热量在其表面的分布情况。 Assume 假设

1. A width to length ratio of W/L for the oven which is rectangular in shape. 1，烤箱是矩形的，长为l，宽为W。

2. Each pan must have an area of A. 2，每个盘子的面积为A。

3. Initially two racks in the oven, evenly spaced. 3，烤箱里有两个置物架，且均匀放置。

Develop a model that can be used to select the best type of pan (shape) under the following conditions:

建立模型，选择出分别满足下列条件的最优解决方法（盘子的形状）：

1. Maximize number of pans that can fit in the oven (N) 1，烤箱里能够安放最多的盘子（N）。

2. Maximize even distribution of heat (H) for the pan 2，盘子上的热量能够最大限度的分布均匀（H）。

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.

3，当1，2两个条件的权重为p与（1-p）时，所得结果随W/L和p的值是怎样变化的。

In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.

除了你的MCM就决方法外，准备一到两页的广告页给新的布朗尼美食杂志，着重表现你的设计和结果。