数学搜索引擎美国数学建模比赛题目及翻译

2020年11月19日发(作者：夏翔)
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 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.

Assume
1. 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 advertising sheet for the new Brownie Gourmet Magazine
highlighting your design and results.
PROBLEM B: Water, Water, Everywhere

Fresh water is the limiting 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 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
feasibility and costs, and why it is the “best water strategy
choice.”