2020年美國HiMCM數學建模競賽A題中英文

文章目錄[隱藏]

中文賽題：最佳暑期工作
英文賽題：The Best Summer Job

中文賽題：最佳暑期工作

雖然現在才11月份，但你需要開始為(wei) 2021年的暑期工作做計劃。今年你有各種各樣的選擇，但你想找出其中“最佳”的選擇。你向你的數學建模小組提出了這個(ge) 問題：

我們(men) 有很多暑期工作的機會(hui) 。有些允許我們(men) 在家線上工作，有些則需要步行或騎自行車，而另一些則要求我們(men) 開車或乘列車才能到達工作地點。每個(ge) 工作每周提供不同的小時數，並且時薪也有所不同。其中一些涉及體(ti) 育活動，或至少不坐在辦公桌前（例如，商店的收銀員，救生員或餐廳的服務員），而另一些則通常是久坐的，並可能需要分析和組織能力（例如，數據分析，辦公室管理，或研究）。

讓我們(men) 建立一個(ge) 模型來評估我們(men) 對暑期工作的選擇，幫助我們(men) 找到“最好”的工作。雖然我們(men) 想掙錢和攢錢，但我們(men) 也希望有時間進行娛樂(le) 活動（例如鍛煉、郊遊、社交）。讓我們(men) 建立一個(ge) 模型，來幫助所有高中生思考和分析他們(men) 的暑期工作選擇。

找暑期工作的高中生應該考慮哪些因素？列出並描述你們(men) 團隊確定的各種因素。請注意，因素可以是定量的或定性的，常數或變量，以及確定性的或概率性的。因素需要包括適當的單位。
利用你們(men) 確定的因素來建立一個(ge) 模型或算法（或一組模型/算法），供高中生根據自己的情況和偏好（作為(wei) 模型的輸入）來評估他們(men) 的暑期工作選擇。
使用合理的數據創建至少十個(ge) 虛構人物，並用這些虛構人物來測試你的模型。解釋你是如何創建這些虛構人物，以及你所選擇的數據。分析你的模型在這些虛構人物身上的應用結果。
描述並展示您將如何演示您的模型，以供他人理解和使用。例如，您可以使用網頁、應用程序或校報文章。注意：你不需要發布一個(ge) 實際的網頁或開發一個(ge) 實際的應用程序，而是描述並提供你所提議的演示方式的布局。

你們(men) 的（PDF格式）論文頁數不能超過25頁，並且應該包括：

一頁摘要。
目錄。
你們完整的解題過程。
參考文獻。

注意：HiMCM 競賽現在有25頁的限製。你提交的論文所有部分（摘要、目錄、參考文獻和任何附錄）的總頁數必須控製在25頁以內(nei) 。

詞匯表：

確定性：隻有一個(ge) （預定）結果的過程。
虛構：不是真實的；人為(wei) 虛構的。
概率性：基於(yu) 概率理論或隨機性在預測未來事件中起作用的過程。
久坐：長時間坐著，並很少活動。

英文賽題：The Best Summer Job

Although it's only November, you need to start planning for your 2021 summer job. You have a variety of choices this year and want to determine your "best" choice. You pose this problem for your team of math friends:

We have many opportunities for a summer job. Some allow us to work from home virtually/electronically, some are a walk or bike ride away, and others require us to drive or take a train. Each job offers differing numbers of hours each week and the hourly rates also vary. Some involve physical activity, or at least not sitting at a desk (e.g. cashier at a store, lifeguarding, or wait staff at a restaurant), while others are mostly sedentary and perhaps use analytical and organizational skills (e.g. data analysis, office administration, or research).

Let's develop a model that will evaluate the choices we have for our summer jobs and help us all find the "best" job. While we certainly want to earn and save some money, we also want to have time for recreation activities (e.g. exercise, outings, and social time with friends). Let's make our model one that will be helpful for all high school students to think about and analyze their summer job options.

What factors should high school students who are looking for a summer job consider? List and describe the various factors your team identifies. Note that factors may be quantitative or qualitative, constant or variable, and deterministic or probabilistic. Be sure to include units as appropriate.
Use your factors to develop a model or algorithm (or set of models/algorithms) for a high school student to use to evaluate their summer job options based on their own situation and preferences as inputs to your model.
Test your model with at least ten fictional persons that you create with reasonable data. Explain your development of these fictional persons and the data you chose. Analyze the results of the application of your model on these persons.
Describe and show how you would present your model for a person to understand and use. For example, you might use a webpage or an app or a school newspaper article. NOTE: You do not need to publish an actual webpage or develop an actual app, but describe and provide the layout of your proposed presentation.

Your PDF solution of no more than 25 total pages should include:

One-page Summary Sheet.
Table of Contents.
Your complete solution.
References list.

Note: The HiMCM Contest now has a 25 page limit. All aspects of your submission count toward the 25 page limit (Summary Sheet, Table of Contents, Reference List and any Appendices).

Glossary:

Deterministic: processes that have only one (predetermined) outcome.
Fictional: not real or true; made up.
Probabilistic: processes based on the theory of probability or that randomness plays a role in predicting future events.
Sedentary: characterized by much sitting and little physical activity.