2022年美国 HiMCM/MidMCM（高中生/初中生）数学建模竞赛赛题发布

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摘要: 2022 HiMCM Problem A: The Need for Bees (and not just for honey) Honeybees, along with a few other key animals, are critical to human existence on our planet. Along with honey production, these ...

2022 HiMCM
Problem A: The Need for Bees (and not just for honey)
Honeybees, along with a few other key animals, are critical to human existence on our planet. Along with
honey production, these insects provide the vital role of pollination of many trees and plants that provide
food for our survival. In 2007, the term Colony Collapse Disorder (CCD) was created to describe the
decline of honeybee populations around the world.[1] Bee decline can be attributed to factors such as
viruses, pesticides, predators, habitat destruction, and environmental conditions.
Some information to consider (but you may find other helpful information online):
 Honeybees can travel up to 20 km, but
typically stay within 6 km of their hive.[2]
 A typical honeybee hive contains between
20,000 and 80,000 honeybees.
 A single honeybee can visit approximately
2,000 flowers or more in a single day.
 Because of the high workload during
summertime, most honeybees work
themselves to death, resulting in a shorter
lifespan.
 During autumn and wintertime, honeybees
may live a bit longer (four to six months).
 A honeybee’s level of activity, pollen consumption, and protein abundance impacts its lifespan.
Requirements
1. Develop a model to determine the population of a honeybee colony over time.
2. Conduct sensitivity analysis on your model to determine which factors (e.g., lifespans, egg laying
rates, fertilized/unfertilized egg ratios, or other factors) have the greatest impact on honeybee
colony size.
3. Model and predict how many honeybee hives you will need to support pollination of a 20-acre
(81,000 square meters) parcel of land containing crops that benefit from pollination.
4. Create a non-technical, one-page blog or infographic for a website that provides the information
you developed.
Your PDF solution of no more than 25 total pages should include:
 One-page Summary Sheet.
 Table of Contents.
 Your complete solution.
 One-page blog or infographic.
 References list.
Note: The HiMCM Contest has a 25-page limit to your PDF solution submission. All aspects of your
submission count toward the 25-page limit (Summary Sheet, Table of Contents, Reference List, and any
Appendices).
References
[1] Yanes, J. (2021). The Devastating Consequences of a World Without Bees. Openmind [Internet].
www.bbvaopenmind.com/en/science/bioscience/consequences-a-world-without-bees.
[2] Greenwood, D. (2022). How Far Do Bees Travel? BeehiveHero [Internet].
https://beehivehero.com/how-far-do-bees-travel-from-their-hives.

2022 HiMCM
Problem B: CO2 and Global Warming
Prior to the Industrial Revolution, carbon dioxide (CO2) in the
atmosphere was consistently around 280 parts per million (ppm).
The concentration of CO2 in the atmosphere reached 377.7 ppm
in March of 2004, resulting in the largest 10-year average
increase up to that time.[1] According to scientists from National
Oceanographic and Atmospheric Administration (NOAA) and
Scripps Institution of Oceanography (SIO) the monthly mean
CO2 concentration level peaked at 421 ppm in May 2022.[2] An
Organisation for Economic Co-Operations and Development
(OECD) report predicts a CO2 level of 685 ppm by 2050.[3]
The editors of Scientific Today magazine have asked your team to address these claims of the
current reported and future predictions of CO2 concentration levels. They provided two data
sets (CO2 Data Set 1 & Temps Data Set 2) to assist in your research.
Requirements
1. Do you agree with CO2 level claims? Use CO2 Data Set 1 to analyze CO2 changes.
a. Do you agree that the March 2004 increase of CO2 resulted in a larger increase than
observed over any previous 10-year period? Why or why not?
b. Fit various (more than one) mathematical models to the data to describe past, and predict
future, concentration levels of CO2 in the atmosphere.
c. Use each of your models to predict the CO2 concentrations in the atmosphere in the year
2100. Do any of your models agree with claims and predictions that the CO2 concentration
level will reach 685 ppm by 2050? If not by 2050, when do your models predict the
concentration of CO2 reaching 685 ppm?
d. Which model do you consider most accurate? Why?
2. What’s the relationship between temperature and CO2? Many scientists think that there is a
relationship between warming global temperatures and the concentration of CO2 in the atmosphere.
Use your work in part 1 and Temps Data Set 2 to assist in your comparison of land-ocean
temperatures and CO2 concentration levels.
a. Build a model to predict future land-ocean temperatures changes. When does your model
predict the average land-ocean temperature will change by 1.25°C, 1.50°C, and 2°C
compared to the base period of 1951-1980?
b. Build a model to analyze the relationship (if any) between CO2 concentrations and land
ocean temperatures since 1959. Explain the relationship or justify that there is no
relationship.
c. Extend your model from part 2.b. into the future. How far into the future is your model
reliable? What concerns, if any, do you have with your model’s ability to predict future CO2
concentration levels and/or land-ocean temperatures?
3. Prepare a non-technical article (1 page maximum) for Scientific Today to explain in your
team’s findings and possible recommendations for the future.
Photo credit: pixabay.com Your PDF solution of no more than 25 total pages should include:
 One-page Summary Sheet.
 Table of Contents.
 Your complete solution.
 One-page non-technical Article.
 References list.
Note: The HiMCM Contest has a 25-page limit. All aspects of your submission count toward the
25-page limit (Summary Sheet, Table of Contents, Reference List, Article, and any Appendices).
Attachment
2022_HiMCM_Data.xlsx
Sheet 1: CO2 Data Set 1
Sheet 2: Temps Data Set 2
References
[1] National Oceanographic and Atmospheric Administration. NOAA Earth System Research
Laboratory. (2022, October). Trends in atmospheric carbon dioxide [Internet].
https://gml.noaa.gov/ccgg/trends/data.html.
[2] National Oceanographic and Atmospheric Administration. NOAA Research News & Features.
(2022, June 3). Carbon dioxide now mare than 50% higher than pre-industrial levels [Internet].
https://www.noaa.gov/news-release/carbon-dioxide-now-more-than-50-higher-than-pre-industrial
levels.
[3] Organisation for Economic Co-Operations and Development. (2012). The OECD environmental
outlook to 2050 [Internet].
https://www.oecd.org/env/cc/Outlook%20to%202050_Climate%20Change%20Chapter_HIGLIGH
TS-FINA-8pager-UPDATED%20NOV2012.pdf.

| ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com |CO2 Data Set 1: Annual month of March averages of CO2 expressed as a mole fraction in dry air,
micromole/mol, abbreviated PPM (parts per million) derived from continuous air samples for the
Mauna Loa Observatory, Hawaii, U.S.A.
Year PPM Year PPM Year PPM
1959 315.98 1980 338.76 2001 371.32
1960 316.91 1981 340.12 2002 373.45
1961 317.64 1982 341.48 2003 375.98
1962 318.45 1983 343.15 2004 377.7
1963 318.99 1984 344.87 2005 379.98
1964 319.62 1985 346.35 2006 382.09
1965 320.04 1986 347.61 2007 384.02
1966 321.37 1987 349.31 2008 385.83
1967 322.18 1988 351.69 2009 387.64
1968 323.05 1989 353.2 2010 390.1
1969 324.62 1990 354.45 2011 391.85
1970 325.68 1991 355.7 2012 394.06
1971 326.32 1992 356.54 2013 396.74
1972 327.46 1993 357.21 2014 398.81
1973 329.68 1994 358.96 2015 401.01
1974 330.19 1995 360.97 2016 404.41
1975 331.13 1996 362.74 2017 406.76
1976 332.03 1997 363.88 2018 408.72
1977 333.84 1998 366.84 2019 411.66
1978 335.41 1999 368.54 2020 414.24
1979 336.84 2000 369.71 2021 416.45
Data Source Credit: National Oceanographic and Atmospheric Administration (NOAA) GML
Data and Scripps Institution of Oceanography (SIO).
https://gml.noaa.gov/webdata/ccgg/trends/co2/co2_annmean_mlo.txt.

| ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com || ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com |
Temps Data Set 2: Global annual mean surface-air temperature change in degrees Celsius based on
land and ocean data compared to the temperature mean of the base period 1951-1980. For example,
in 2021, the global land and sea temperature was 0.84°C above the temperature mean of the base
period of 1951-1980.
Data Source Credit: National Aeronautics and Space Administration Goddard Institute for Space
Studies.
 GISTEMP Team, 2022: GISS Surface Temperature Analysis (GISTEMP), version 4. NASA
Goddard Institute for Space Studies. Dataset accessed 2022-10-18
at data.giss.nasa.gov/gistemp/.
 Lenssen, N., G. Schmidt, J. Hansen, M. Menne, A. Persin, R. Ruedy, and D. Zyss,
2019: Improvements in the GISTEMP uncertainty model. J. Geophys. Res. Atmos., 124, no.
12, 6307-6326, doi:10.1029/2018JD029522.

2022 MidMCM
Problem C: Polygon Paradise Park
Note: Only teams with all members younger than 14 ½ years old may choose Problem C.
A group of four friends want to go to Polygon Paradise Park next summer. Polygon Paradise
Park is a small amusement park open from 9am to 9pm. The park has ten rides of different types
and thrill levels. The Trapezoid Show, a location with several different performances throughout
the day, offers a circus acrobatics show, a magic show, and evening fireworks. The Games
building has both arcade and carnival games. Food options include the Triangle Restaurant, the
hot dog stand, and the ice cream cart. The hot dog stand and the ice cream cart are “take away”
options, while the Triangle Restaurant requires 30-60 minutes to sit at a table and enjoy a meal.
The restrooms (WC) are centrally located in the park for easy access. Visitors can purchase
souvenirs in the gift shop located near the park entrance.
The group has hired your team at the MidMCM Travel Agency to make sure each member has a
great time during their one-day trip to this amusement park. Your team is to develop a schedule
to make the group’s day at the park the best possible. The group has provided you with the
following information.
● Ming loves to play games and win prizes. Ming gets motion sick on fast moving rides,
especially after eating.
● Ishmael loves roller coasters and wants to ride as many of them as possible during the day.
Ishmael also likes performing card tricks and is interested in seeing the magic show.
● Karine is very impatient and hates waiting in long lines. Karine wants to attend the circus
acrobatics show. Karine does not eat hot dogs.
● Freya likes to spend time on water rides to cool off. Freya likes to go with the flow and is
happy spending time with friends. Freya wants to make sure she gets a souvenir to remember
the trip.
| ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com | Your planning resources from MidMCM Travel Agency include a show schedule for the
Trapezoid Show location, tables containing ride categories and durations, expected ride wait
times throughout the day, food options and wait times, and a map of the park. These resources
are included at the end of the problem statement.
Requirements
1. Get Started. Familiarize yourself with Polygon Paradise Park and the group of friends.
a. What does the Polygon Paradise Park have to offer this group of friends to enjoy a
great day at the park?
b. Given the information about the friends, what considerations do you need to
incorporate into your plan? For example, you should be able to make some
assumptions about how each would most like to spend their day.
c. Describe an ideal day at the park for each of the friends.
2. Create the Schedule. The group of friends would like to spend most of the day together as a
group of four. They are willing to split up into groups of two for up to 4 hours of the day if it
will increase everyone’s enjoyment of the trip.
a. Make a list of the various activities you need to include into your schedule.
b. What are the times required for those activities? For example, to walk from one
location to another. Don’t forget that a whole day at the park might require time to
eat and use the restroom (WC).
c. Identify and describe any activities that might require the group to split up to
increase enjoyment. Explain.
d. Create a detailed schedule for the group of friends to use as a guide for their day at
Polygon Paradise Park.
3. Share Your Schedule. Write a one- to two-page letter to the group of friends that describes
the highlights of your recommended schedule and explains why it will offer the best possible
day at Polygon Paradise Park.
4. Reflect. How is the schedule for Ming, Ishmael, Karine, and Freya different from a schedule
you might create for your own MidMCM team to go to the park? Could you use the process
you used to create the schedule for Ming, Ishmael, Karine, and Freya to create a schedule for
your MidMCM team? (You do not need to create an actual schedule for your team, but you
need briefly describe the process and what would be different!)
Your MidMCM PDF solution document should include the following:
a. One-page Summary Sheet.
b. Table of Contents.
c. Your complete solution to the problem and requirements. See MidMCM
Guidance at the end of this document.
| ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com | d. One- to two-page letter to the group of friends.
e. References List (for example, any websites you used to gather information).
There is no specific required page length for a complete MidMCM submission. You may use up
to 25 total pages for all your solution work and any additional information you want to include
(for example: drawings, diagrams, calculations, tables). Partial solutions are accepted.
Glossary
Assumptions: hypotheses or educated guesses that take the place of an unknown or
uncertain piece of information.
Restrooms (WC): A facility containing flush toilets; sometimes called a bathroom or a
water closet (WC).
Take Away: food and drink vendors where you can purchase food and drinks that can be
easily consumed while walking to your next destination.
Resources
Trapezoid Show Schedule
Time Show Duration
10 am Circus Acrobatics 1 hour
12 pm Circus Acrobatics 1 hour
2 pm Magic Show 1 hour
4 pm Circus Acrobatics 1 hour
6 pm Magic Show 1 hour
8 pm Firework Show 1 hour
Ride Information
Name of Ride/Activity Ride Type/Activity Duration
Heptagon Coaster Extreme Thrill 2.5 min
Decagon Coaster Extreme Thrill 3.0 min
Rhombus Ride Extreme Thrill 4.0 min
Hexa-Swings Medium Thrill 2.0 min
Pentagon Bumpers Medium Thrill 5.0 min
Square Scramble Medium Thrill 2.5 min
Concave Train Basic 15.0 min
Starburst Carousel Basic 3.0 min
Dodecagon Rapids Water 10.0 min
Octagon Flume Water 5.0 min

| ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com | | ©2022 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com |
Ride Wait Times (Minutes)
Time
9:00 AM
0
0
0
0
0
0
0
0
0
0
10:00 AM
5 15 0 10 0 10 0 5 0 10
11:00 AM
10
30
5
20
5
10
5
10
5
15
12:00 PM
15 45 10 30 10 10 5 15 10 15
1:00 PM
10
60
15
40
10
30
5
10
10
10
2:00 PM
10 75 20 40 15 60 10 10 10 5
3:00 PM
15
75
15
30
15
60
10
15
10
5
4:00 PM
15 60 10 30 10 60 10 10 10 5
5:00 PM
15
45
5
20
10
30
10
10
10
5
6:00 PM
5 30 0 20 5 10 5 5 5 5
7:00 PM
5
30
0
10
0
10
0
5
5
5
8:00 PM
5 15 0 10 0 0 0 5 5 5
9:00 PM
5
0
0
10
0
0
0
5
0
0
Food Options
Name Types of Food Hours of Operation
Hot Dog Stand Take Away 10:00 AM – 9:00 PM
Ice Cream Cart Take Away 11:00 AM – 9:00 PM
Triangle Restaurant Sit Down 9:00 AM – 8:00 PM
Food Wait Times (Minutes)
Time
9:00 AM
Closed
Closed
0
10:00 AM
0 Closed 5
11:00 AM
5
0
30
12:00 PM
10 5 60
1:00 PM
10
10
20
2:00 PM
5 15 0
3:00 PM
0
15
0
4:00 PM
5 10 10
5:00 PM
10
5
40
6:00 PM
10 5 60
7:00 PM
10
5
10
8:00 PM
5 0 0
9:00 PM
5
0
0
Concave
Train
Decagon
Coaster
Dodecagon
Rapids
Heptagon
Coaster
Hexa
Swings
Octagon
Flume
Pentagon
Bumpers
Rhombus
Ride
Square
Scramble
Star Burst
Carousel
Hot Dog
Stand
Ice Cream
Cart
Triangle
RestaurantPolygon Paradise Park
DECAGON COASTER
CONCAVE TRAIN
MAIN
ENTRANCE
OCTAGON
FLUME
HEXA
SWINGS
RHOMBUS
RIDE
WC
DODECAGON RAPIDS
TRIANGLE
RESTAURANT
G
A
M
E
S
SQUARE
SCRAMBLE
Hot Dogs
ICE
CREAM
STAR
BURST
CAROUSEL
HEPTAGON COASTER
= ENTRANCE / EXIT
0 50m 100m
SCALE: 1 Centimeter = 25 Meters
Copyright © 2022 COMAP, Inc.
GIFT SHOP
PENTAGON
BUMPERS
TRAPEZOID SHOWGuidance for MidMCM
COMAP has a Judges’ Commentary article about the 2021 MidMCM along with the two Outstanding
2021 MidMCM papers at https://www.mathmodels.org/Problems/2021_MidMCM_Commentary.pdf.
The commentary article provides guidance to both advisors and students. We also provide the following
general guidance about MidMCM submission organization.
Solutions must be in PDF format and submitted in one PDF document. However, this does not preclude
MidMCM teams from doing mathematics, graphs, tables, sketches, etc. by hand and including pictures of
their work in the single PDF document submission. As students move to high school and the HiMCM, we
expect that submissions will be typed. For the MidMCM, advisors may technically assist students in
putting their solution components into one PDF format file for submission.
As with HiMCM, there is a 25-page limit for the submission document. This does not mean your solution
must be 25 pages. A shorter submission is certainly acceptable. All portions of your submission (text,
graphs, tables, charts, pictures, etc.) must be within one PDF document that is 25 pages or less. We accept
partial solutions.
In general, a complete solution submission is organized as follows:
Executive Summary – Write this summary after you have done all your work. This one-page summary is
Page #1 of your solution document. It provides an overview of your work and includes actual results.
Table of Contents – List the major items in your solution document to show the organization of your
paper.
Introduction and Restatement of the Problem – Introduce the problem. Restate the problem and
requirements in your own words.
Assumptions with Justifications – State any assumptions you made to simplify and solve the problem
and state why you made those assumptions.
Variable Definitions – Define any variables you use in your model and equations.
Presentation of Model and Solution – Ensure you address all requirements and describe what you are
doing in solving the problem. Show and explain all your work. Use representations that help you tell the
reader how you solved the problem (for example: equations, tables, graphs, pictures, etc.).
Analysis of Your Work – Address any strengths (good points) and limitations (weaknesses) of your
model and solution.
Concluding Paragraph – End your solution paper with a final concluding paragraph that summarizes
your results and/or makes recommendations for future work.
Reference List – List any sources that you used to solve the problem (for example, website pages,
newspaper, or magazine articles, etc.).