2021年美国HiMCM数学建模竞赛C题中英文

中文赛题：遛狗公园

遛狗公园在美国和加拿大越来越受欢迎。加拿大阿尔伯塔省的卡尔加里市为 130 万居民提供了 10 个遛狗公园，美国爱达荷州的博伊西市为每 10 万居民提供 6.3 个遛狗公园！

由于遛狗公园为狗、狗的主人以及社区带来了很多好处，遛狗公园的需求在不断增长。遛狗公园通常是一个有围栏的户外区域，在那里人们可以和他们的狗一起玩耍。遛狗公园允许狗在一个安全和受控的环境中散步、锻炼和自由玩耍（不拴绳）。遛狗公园就像是狗的游乐场。此外，狗主人可以在他们的狗玩耍时自由社交。这可以帮助新居民建立社区联系，并促进现有邻里间的交流。

很像游乐场，遛狗公园有很多形状和大小，这主要取决于可用的空间和资金。如果有足够的空间，大狗和小狗可以在分格开的区域玩耍。一些狗主人喜欢这种分格，另一些则喜欢让各种大小的狗一起玩耍。一些遛狗公园有照明，而另一些只在白天开放。简单的遛狗公园可能只是一个有围栏的开放空间，而其他更精致的遛狗公园可能还有各种各样的设施和狗玩设备。

米德尔维尔镇公园及娱乐事务署署长请求你的团队制定一项计划：在图 1 所示的地点修建米德尔维尔遛狗公园。署长提出了以下要求：

1. 你可以在图 1 中蓝色区域内的任何位置设立遛狗公园。
2. 遛狗公园的总面积最大为 1 英亩（43560 平方英尺，4046.8 平方米）。
3. 必须将现有滑板公园保持在其当前位置。

图1：遛狗公园位置区域

1. 规划你的遛狗公园

a. 安全遛狗公园的必要特征是围栏、供水和垃圾桶。还有许多其他特征，你可能想包括在你的遛狗公园中。列出你想为狗狗公园考虑的所有特征。

b. 现在考虑为了规划和设计你的遛狗公园，你必须要做出的决定。你需要解决的一些问题可能是：

• 遛狗公园的形状和大小？
• 你将在可用区域（图1）的何处设置你的遛狗公园？
• 建造这个遛狗公园需要什么材料？
• 建造和维护遛狗公园需要多少钱？

c. 描述一下你的遛狗公园。你的描述需要包括你的遛狗公园包括哪些功能，回答需要你解决的问题，并做出必要的决定（根据你在第 1.a 和 1.b 部分中的工作）。

2. 设计你的遛狗公园

a. 绘制一张你的遛狗公园比例图，图中包括你决定为遛狗公园配备的所有特征。在图形上标出尺寸，并注意比例。你可以手绘出你的遛狗公园，也可以借用电脑软件来绘制。

b. 建筑商通常使用物料清单（BOM）列出项目所需的材料和物品，以及数量和成本。一个物料清单的实例如表1所示。

表 1: 物料清单（BOM）实例

使用你绘制的比例图来为遛狗公园项目创建物料清单。

c. 除了物料清单中显示的材料和物品的成本外，你还需要列出并描述建造和维护你的遛狗公园所需的任何其他费用。

d. 有时候，在制定计划之后，你需要做一些调整。如果米德尔维尔镇决定为遛狗公园提供比你计划的更多或更少的空间怎么办？如果他们提供的钱比你决定的要多或要少，你该怎么办？与其重新规划设计，你如何调整现有的遛狗公园计划？写一段关于如何推广你的遛狗公园计划，使你的计划具有可扩展性。

3. 展示你的遛狗公园计划

写一封一页纸的信给米德尔维尔镇公园及娱乐事务署署长，描述你的遛狗公园及其特点。说明你的遛狗公园的可扩展性。

您的 MidMCM PDF 解决方案（论文）应包括以下内容：

• 一页的摘要（总结）。
• 目录。
• 你对问题的完整解决方案。
• 给米德尔维尔镇公园及娱乐事务署署长的一页信。
• 参考文献列表（例如，用于收集信息的任何网站）。

完整的 MidMCM 作品（论文）没有特定的页面长度要求。对于所有解决方案以及任何要包含的附加信息（例如：图形、图表、计算、表格），最多不超过 25 页。只解决部分问题的方案是可以接受的。

词汇表

假设：代替未知信息的假设或有根据的猜测。

材料清单（BOM）：完成给定项目所需的所有零件、项目、原材料等及其成本的完整清单。

推广：使计划不那么具体，更具有一般性。

维护：随着时间的推移保持清洁和安全。

可扩展：在大小或比例上改变某物的能力（例如，变大或变小）。

比例图：按比例缩小或增大的真实对象的图。图形中使用的比例称为比例尺。

英文赛题：Dog Park

Dog parks are becoming increasingly popular in the United States and Canada. The city of Calgary in Alberta, Canada has 10 dog parks for a city of 1.3 million residents, and the city of Boise in Idaho, US has 6.3 dog parks per 100,000 residents!

Considering the benefits they provide to dogs, their owners, and communities, the growth in demand for dog parks is not surprising. A dog park is typically a fenced-in outdoor area where people and their dogs can play together. Dog parks allow dogs to roam, exercise, and play off-leash in a safe and controlled environment. It’s like a playground for dogs. Moreover, dog owners are free to socialize while their dogs are playing. This can help new residents establish community connections and allows existing neighbors to stay connected.

Much like playgrounds, dog parks come in many shapes and sizes depending on the space and money available. With enough space comes the option to have separate spaces for large and small dogs. Some owners prefer this separation, while others prefer to have dogs of all sizes play together. Some dog parks have lighting, while others only operate during daylight hours. Basic dog parks may have little more than a fenced in open space, while other more elaborate dog parks may have a wide variety of amenities and dog play equipment.

The Town of Middleville Director of Parks & Recreation has asked your team to develop a plan to build the Middleville Dog Park at the site shown in Figure 1. The Director provided the following guidance:

1. You may locate the dog park anywhere within the area outlined in blue in Figure 1.
2. The dog park may be up to 1-acre (43,560 square feet) in total size.
3. You must keep the existing skateboard park in its current location.

Figure 1: Area for Location of Dog Park

1. Planning Your Dog Park

a. The necessary features of a safe dog park are fencing, a water supply, and trash cans. There are many other features that you might want to include in your dog park. Make a list of all the features you want to consider for your dog park.

b. Now think about the decisions you must make to plan and design your dog park. A few of your questions might be:

• What shape and how big will the dog park be?
• Where in the available area (Figure 1) will you locate your dog park?
• What materials will you need to build the park?
• How much will it cost to build and maintain the dog park?

c. Describe your dog park. To do this you will need to decide what features you will include, answer your questions, and make necessary decisions (from your work in Parts 1.a. and 1.b.).

2. Designing Your Dog Park

a. Make a scale drawing of your dog park that includes all the features you decide to include. Label your drawing with measurements and be sure to note your scale. You can hand-draw your dog park or use technology to do so.

b. Builders often use a Bill-Of-Materials (BOM) to list the materials and items needed for a project, along with quantities and costs. An example of a BOM with a sample entry is shown in Table 1.

sample entry is shown in Table 1.

Table 1: Sample Entry for Bill-Of-Materials (BOM)

Use your scale drawing to create a BOM for your dog park project.

Use your scale drawing to create a BOM for your dog park project.

c. In addition to the cost of the materials and items shown in your BOM, list and describe any other expenses necessary to build and maintain your dog park.

d. Sometimes after developing your plan, you need to make some adjustments. What if Middleville decided to provide more or less space for the dog park than you planned? What if they provided more or less money than you decided you needed to build the park? Rather than starting over, how could you adjust your existing dog park plan? Write a paragraph about how you could generalize your dog park plan so that it is scalable.

3. Sharing your dog park plan

Write a one-page letter to the Middleville Director of Parks & Recreation describing your dog park and its features. Address the scalability of your dog park.

Your MidMCM PDF solution document should include the following:

• One-page Summary Sheet.
• Table of Contents.
• Your complete solution to the problem and requirements.
• One-page letter to the Middleville Director of Parks & Recreation.
• 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

Assumption: a hypothesis or educated guess that takes the place of an unknown piece of information.Bill-Of-Materials (BOM): a complete list of all required parts, items, raw materials, etc. needed to complete a given project, along with their costs.Generalize: make something less specific.Maintain: keep clean and safe over time.Scalable: the ability to change something in size or scale (for example, make larger or smaller).Scale Drawing: a drawing of a real object that has been made smaller or larger proportionally. The proportion used in the drawing is called the scale ratio.