**2013
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). 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.”

Countries: United States, China, Russia, Egypt, or Saudi Arabia

**2013 ICM Problem**

**PROBLEM C: ****Network Modeling of Earth's Health**

**Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a
maximum of 21 pages.**

**Click the title below to download a PDF of the 2013 ICM Problem.**

Network Modeling of Earth's Health