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MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling
2005
MCM Problems
PROBLEM A: Flood Planning
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?
PROBLEM B: Tollbooths
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.
2005 ICM Problem
PROBLEM C:
Nonrenewable Resources
Select a vital
nonrenewable or exhaustible resource (water, mineral, energy,
food, etc.) for which your team can find appropriate world-wide
historic data on its endowment, discovery, annual consumption,
and price.
The modeling
tasks are:
- Using the
endowment, discoveries, and consumption data, model the
depletion or degradation of the commodity over a long horizon
using resource modeling principles.
- Adjust the
model to account for future economic, demographic, political
and environmental factors. Be sure to reveal the details of
your model, provide visualizations of the model’s output, and
explain limitations of the model.
- Create a
fair, practical "harvesting/management" policy that may
include economic incentives or disincentives, which sustain
the usage over a long period of time while avoiding severe
disruption of consumption, degradation or rapid exhaustion of
the resource.
- Develop a
"security" policy that protects the resource against theft,
misuse, disruption, and unnecessary degradation or destruction
of the resource. Other issues that may need to be addressed
are political and security management alternatives associated
with these policies.
- Develop
policies to control any short- or long-term "environmental
effects" of the harvesting. Be sure to include issues such as
pollutants, increased susceptibility to natural disasters,
waste handling and storage, and other factors you deem
appropriate.
- Compare this
resource with any other alternatives for its purpose. What new
science or technologies could be developed to mitigate the use
and potential exhaustion of this resource? Develop a research
policy to advance these new areas.
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