Check out the live text-chat for this problem that happened on Wednesday, February 10, 2021 from 10:00 – 11:30 a.m. EST with the problem author in the “Comments” section below!
As society begins its slow crawl back to a pre-pandemic “normal,” there are bound to be some things that simply do not return to the way they were a year ago. For example, during the pandemic, some businesses took major hits (travel industry, car repair, brick-and-mortar shopping) while others have seen a boom (home remodeling, recreational vehicles, delivery services). Likewise, the fitness industry had its ups (at-home gym equipment sales and bicycle sales) and downs (in-person training facilities). And these are just two of the many areas where significant changes occurred. Which of those that struggled might return stronger, and will those that saw their profits increase continue that success?
You and your team are being asked to choose a single industry that has experienced drastic changes caused directly by the pandemic and address one question: will those changes last? A few potential industries are listed below, but the list is not exhaustive—your team is encouraged to choose a field and scenario that you find both interesting and meaningful to you.
Potential industries:
- Restaurant industry (in-person dining versus carryout/delivery)
- Travel industry (vacation air travel versus vacationing by car)
- Health industry (telehealth versus in-person visits)
- Colleges (in-person versus online courses)
- Recreation (natural areas (state/national parks) versus man-made attractions (amusement parks)
- Personal fitness (self-guided fitness (running/cycling/walking/YouTube fitness) versus gyms/group training classes)
- Entertainment (film industry: movie theater releases versus direct-to-streaming releases)
Instead of the M3 Challenge’s typical three sub-question format, your team is asked to mathematically investigate the changes by completing the following steps.
- Choose an industry and develop a model that takes into account the operation of the industry and outputs a success metric. Consider a variety of variables/parameters that have changed over the past year. How does the performance of the industry differ when you use pre- and during-pandemic values?
- Use/adjust your models to predict how the industry evolves over the next five years. Will the changes be permanent, will they revert to pre-pandemic levels, or something else altogether? Include a measure of how significantly the pandemic affects the industry in the long term.
While being very open-ended, this practice problem is intended to help your team focus on some of the non-mathematical aspects of the modeling process. Yes, part of this problem asks for mathematical analysis, but before you can begin that work, you must properly frame your question; make clear, appropriate, and justified assumptions; and think widely about the variables of importance.
Additionally, while some data is typically provided for M3 Challenge problems, there is no specific data being made available here. That should in no way distract you from attacking your team’s chosen topic. Do not waste much time scouring the web for obscure data sources; simply assume you have the data that you need and build your math model accordingly.
Problem Author: Dr. Neil Nicholson, North Central College
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