2021年美國HiMCM數學建模競賽C題中英文

中文賽題：遛狗公園

遛狗公園在美國和加拿大越來越受歡迎。加拿大阿爾伯塔省的卡爾加裏市為(wei) 130 萬(wan) 居民提供了 10 個(ge) 遛狗公園，美國愛達荷州的博伊西市為(wei) 每 10 萬(wan) 居民提供 6.3 個(ge) 遛狗公園！

由於(yu) 遛狗公園為(wei) 狗、狗的主人以及社區帶來了很多好處，遛狗公園的需求在不斷增長。遛狗公園通常是一個(ge) 有圍欄的戶外區域，在那裏人們(men) 可以和他們(men) 的狗一起玩耍。遛狗公園允許狗在一個(ge) 安全和受控的環境中散步、鍛煉和自由玩耍（不拴繩）。遛狗公園就像是狗的遊樂(le) 場。此外，狗主人可以在他們(men) 的狗玩耍時自由社交。這可以幫助新居民建立社區聯係，並促進現有鄰裏間的交流。

很像遊樂(le) 場，遛狗公園有很多形狀和大小，這主要取決(jue) 於(yu) 可用的空間和資金。如果有足夠的空間，大狗和小狗可以在分格開的區域玩耍。一些狗主人喜歡這種分格，另一些則喜歡讓各種大小的狗一起玩耍。一些遛狗公園有照明，而另一些隻在白天開放。簡單的遛狗公園可能隻是一個(ge) 有圍欄的開放空間，而其他更精致的遛狗公園可能還有各種各樣的設施和狗玩設備。

米德爾維爾鎮公園及娛樂(le) 事務署署長請求你的團隊製定一項計劃：在圖 1 所示的地點修建米德爾維爾遛狗公園。署長提出了以下要求：

1. 你可以在圖 1 中藍色區域內的任何位置設立遛狗公園。
2. 遛狗公園的總麵積最大為 1 英畝（43560 平方英尺，4046.8 平方米）。
3. 必須將現有滑板公園保持在其當前位置。

圖1：遛狗公園位置區域

1. 規劃你的遛狗公園

a. 安全遛狗公園的必要特征是圍欄、供水和垃圾桶。還有許多其他特征，你可能想包括在你的遛狗公園中。列出你想為(wei) 狗狗公園考慮的所有特征。

b. 現在考慮為(wei) 了規劃和設計你的遛狗公園，你必須要做出的決(jue) 定。你需要解決(jue) 的一些問題可能是：

• 遛狗公園的形狀和大小？
• 你將在可用區域（圖1）的何處設置你的遛狗公園？
• 建造這個遛狗公園需要什麽材料？
• 建造和維護遛狗公園需要多少錢？

c. 描述一下你的遛狗公園。你的描述需要包括你的遛狗公園包括哪些功能，回答需要你解決(jue) 的問題，並做出必要的決(jue) 定（根據你在第 1.a 和 1.b 部分中的工作）。

2. 設計你的遛狗公園

a. 繪製一張你的遛狗公園比例圖，圖中包括你決(jue) 定為(wei) 遛狗公園配備的所有特征。在圖形上標出尺寸，並注意比例。你可以手繪出你的遛狗公園，也可以借用電腦軟件來繪製。

b. 建築商通常使用物料清單（BOM）列出項目所需的材料和物品，以及數量和成本。一個(ge) 物料清單的實例如表1所示。

表 1: 物料清單（BOM）實例

使用你繪製的比例圖來為(wei) 遛狗公園項目創建物料清單。

c. 除了物料清單中顯示的材料和物品的成本外，你還需要列出並描述建造和維護你的遛狗公園所需的任何其他費用。

d. 有時候，在製定計劃之後，你需要做一些調整。如果米德爾維爾鎮決(jue) 定為(wei) 遛狗公園提供比你計劃的更多或更少的空間怎麽(me) 辦？如果他們(men) 提供的錢比你決(jue) 定的要多或要少，你該怎麽(me) 辦？與(yu) 其重新規劃設計，你如何調整現有的遛狗公園計劃？寫(xie) 一段關(guan) 於(yu) 如何推廣你的遛狗公園計劃，使你的計劃具有可擴展性。

3. 展示你的遛狗公園計劃

寫(xie) 一封一頁紙的信給米德爾維爾鎮公園及娛樂(le) 事務署署長，描述你的遛狗公園及其特點。說明你的遛狗公園的可擴展性。

您的 MidMCM PDF 解決(jue) 方案（論文）應包括以下內(nei) 容：

• 一頁的摘要（總結）。
• 目錄。
• 你對問題的完整解決方案。
• 給米德爾維爾鎮公園及娛樂事務署署長的一頁信。
• 參考文獻列表（例如，用於收集信息的任何網站）。

完整的 MidMCM 作品（論文）沒有特定的頁麵長度要求。對於(yu) 所有解決(jue) 方案以及任何要包含的附加信息（例如：圖形、圖表、計算、表格），最多不超過 25 頁。隻解決(jue) 部分問題的方案是可以接受的。

詞匯表

假設：代替未知信息的假設或有根據的猜測。

材料清單（BOM）：完成給定項目所需的所有零件、項目、原材料等及其成本的完整清單。

推廣：使計劃不那麽(me) 具體(ti) ，更具有一般性。

維護：隨著時間的推移保持清潔和安全。

可擴展：在大小或比例上改變某物的能力（例如，變大或變小）。

比例圖：按比例縮小或增大的真實對象的圖。圖形中使用的比例稱為(wei) 比例尺。

英文賽題：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.