• The Mathematical Contest in Modeling (COMAP's site for the competition)

• Results of previous Mathematical Contests in Modeling

• The 2004 Mathematical Contest in Modeling

• The 2003 Mathematical Contest in Modeling

• The 2002 Mathematical Contest in Modeling

• The 2001 Mathematical Contest in Modeling

• The 2000 Mathematical Contest in Modeling

• The 1999 Mathematical Contest in Modeling

• The 1998 Mathematical Contest in Modeling

The Mathematical Contest in Modeling is an annual event, sponsored by the Consortium for Mathematics and Its Applications, in which students at colleges and universities all over the world are asked to develop and analyze mathematical models of open-ended, practical problems for which no direct solutions are known. Participants work in teams of three and are permitted to use libraries, computers, and other inanimate sources of knowledge and inspiration. The organizers of the contest propose three problems; over the four days of the contest, each team selects one of these problems, designs, implements, and analyzes a model, and writes a substantial report presenting its results.

The twenty-first Mathematical Contest in Modeling was held on February 3-7, 2005. Grinnell fielded three teams this year:

- Daren Brantley 2005, Andrew Rinne 2006, and Sheng Wang 2008 (faculty sponsor: Charles Cunningham)
- Kate Thomas 2005, Kate Kearney 2005, and Steve Ford 2005 (faculty sponsor: Karen Shuman)
- Norman Perlmutter 2007, Patrick Busch 2008, and Oge Nnadi 2006 (faculty sponsor: Karen Shuman)

Here are the problems that COMAP posed this year. The team comprising Daren Brantley, Andrew Rinne, and Sheng Wang chose to work on problem A, and the other two teams on problem B.

Lake Murray in central South Carolina is formed by a large earthen dam, which was completed in 1930 for power production. Model the flooding downstream in the event there is a catastrophic earthquake that breaches the dam.

Two particular questions:

- Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver from the dam. How much flooding will occur in Rawls Creek from a dam failure, and how far back will it extend?
- Could the flood be so massive downstream that water would reach up to the S.C. State Capitol Building, which is on a hill overlooking the Congaree River?

Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided highways that are interrupted at intervals by toll plazas. Because collecting tolls is usually unpopular, it is desirable to minimize motorist annoyance by limiting the amount of traffic disruption caused by the toll plazas. Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza. Upon entering the toll plaza, the flow of vehicles fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze back down to a number of travel lanes equal to the number of travel lanes before the toll plaza. Consequently, when traffic is heavy, congestion increases upon departure from the toll plaza. When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll.

Make a model to help you determine the optimal number of tollbooths to deploy in a barrier-toll plaza. Explicitly consider the scenario where there is exactly one tollbooth per incoming travel lane. Under what conditions is this more or less effective than the current practice? Note that the definition of “optimal” is up to you to determine.

This year, 828 teams submitted complete entries. Thirteen of these entries were judged Outstanding; one hundred eleven others, Meritorious. Two hundred eighty-four received Honorable Mentions in COMAP's report. The remaining 420 teams were classified as Successful Participants.

All three of Grinnell's teams received the Successful Participant ranking.

This document is available on the World Wide Web as

http://www.math.grinnell.edu/mcm-2005.xhtml