2020年美国HiMCM数学建模竞赛A题中英文

中文赛题：最佳暑期工作

虽然现在才11月份，但你需要开始为2021年的暑期工作做计划。今年你有各种各样的选择，但你想找出其中“最佳”的选择。你向你的数学建模小组提出了这个问题：

我们有很多暑期工作的机会。有些允许我们在家线上工作，有些则需要步行或骑自行车，而另一些则要求我们开车或乘列车才能到达工作地点。每个工作每周提供不同的小时数，并且时薪也有所不同。其中一些涉及体育活动，或至少不坐在办公桌前（例如，商店的收银员，救生员或餐厅的服务员），而另一些则通常是久坐的，并可能需要分析和组织能力（例如，数据分析，办公室管理，或研究）。

让我们建立一个模型来评估我们对暑期工作的选择，帮助我们找到“最好”的工作。虽然我们想挣钱和攒钱，但我们也希望有时间进行娱乐活动（例如锻炼、郊游、社交）。让我们建立一个模型，来帮助所有高中生思考和分析他们的暑期工作选择。

1. 找暑期工作的高中生应该考虑哪些因素？列出并描述你们团队确定的各种因素。请注意，因素可以是定量的或定性的，常数或变量，以及确定性的或概率性的。因素需要包括适当的单位。

2. 利用你们确定的因素来建立一个模型或算法（或一组模型/算法），供高中生根据自己的情况和偏好（作为模型的输入）来评估他们的暑期工作选择。

3. 使用合理的数据创建至少十个虚构人物，并用这些虚构人物来测试你的模型。解释你是如何创建这些虚构人物，以及你所选择的数据。分析你的模型在这些虚构人物身上的应用结果。

4. 描述并展示您将如何演示您的模型，以供他人理解和使用。例如，您可以使用网页、应用程序或校报文章。注意：你不需要发布一个实际的网页或开发一个实际的应用程序，而是描述并提供你所提议的演示方式的布局。

你们的（PDF格式）论文页数不能超过25页，并且应该包括：

• 一页摘要。
• 目录。
• 你们完整的解题过程。
• 参考文献。

注意：HiMCM竞赛现在有25页的限制。你提交的论文所有部分（摘要、目录、参考文献和任何附录）的总页数必须控制在25页以内。

词汇表：

• 确定性：只有一个（预定）结果的过程。

• 虚构：不是真实的；人为虚构的。

• 概率性：基于概率理论或随机性在预测未来事件中起作用的过程。

• 久坐：长时间坐着，并很少活动。

英文赛题：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 mostlysedentaryand 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.

1. 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, anddeterministicorprobabilistic. Be sure to include units as appropriate.

2. 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.

3. Test your model with at least tenfictionalpersons 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.

4. 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.