Powered by Comap

Problem Title: The Ultimate Brownie Pan

  Year: 2013      
  Student Level: Undergraduate      
  Source: MCM      
  Commentary: Yes (1)      
  Student Papers: Yes (7)      

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.

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.


Judges' Commentary: The Ultimate Brownie Pan Papers

Kelly Black
Dept. of Mathematics
Clarkson University

  Student Papers      

Team 18439: Optimize the Shape For Brownie Pan

Fudan University, China


Team 19178: The Ultimate Brownie Pan

Shanghai Jiaotong University, China


Team 20329: Applied Mathematicans Bake the Best Brownies: The Ultimate Pan Design

Peking University, China


Team 20559: Cooking Up the Optimal Baking Algorithm

Bethel University, MN


Team 22550: The Best Rounded Rectangle for Ultimate Brownies

University of Colorado Boulder, CO


Team 23004: The Design of Ultimate Brownie Pan

Shandong University, China


Team 17617: The Ultimate Brownie Pan

Tongji University, China