Problem A Pole vaulting - a story of harmonious combination between man and pole
问题 A 跳高——人与杆的和谐结合的故事

Pole vault is considered one of the most difficult sports. The 6.14-meter world record set by Ukrainian pole vaulter Bubka in 1994 was once considered one of the records to break most hardly, but now the record has been repeatedly broken. On August 25th of this year, at the Silesia station of the World Association of Athletics Federations Diamond League, Swedish pole vault world record holder Duplandis broke his own 6.25-meter jump at the Paris Olympics with an astonishing 6.26-meter result and won the gold medal. In fact, Duplandis has broken his own world records multiple times.
撑杆跳被公认为最困难的运动之一。乌克兰撑杆跳运动员布勃卡在 1994 年创下的 6.14 米世界纪录曾一度被认为是最难打破的纪录之一，但现在这个纪录已经被多次打破。今年 8 月 25 日，在世界田径联合会钻石联赛的西里西亚站，瑞典撑杆跳世界纪录保持者杜普兰迪斯以惊人的 6.26 米成绩打破了他在巴黎奥运会上创下的 6.25 米跳高纪录，并获得了金牌。事实上，杜普兰迪斯已经多次打破了自己的世界纪录。

Technically speaking, pole vaulting involves several main processes, including "Approach Run, plant, takeoff, swing, and clearance ", which are not only related to the athlete's physical features and ability, but also closely related to the pole used. Your team is requesting solutions to the following issues:
从技术角度讲，撑杆跳高包括几个主要过程，包括“助跑、插杆、起跳、摆动和过杆”，这些不仅与运动员的生理特征和能力有关，而且与所使用的撑杆密切相关。您的团队要求解决以下问题：

(1) Collect relevant data, including some physical parameters of athletes, as well as data on the material, mechanical characters, and performance of the poles used.
(1) 收集相关数据，包括运动员的一些物理参数，以及使用杆的材料、力学特性和性能数据。

(2) Establish a mathematical model for the pole vault process and calculate the athlete's performance based on the aforementioned parameters.
(2) 建立撑杆跳高的数学模型，并根据上述参数计算运动员的表现。

(3) Study the relation between the grades and length, material of pole, etc., and also consider the effect on heights, weights, genders and speed of player.
(3) 研究成绩与杆长、材料等的关系，同时考虑对身高、体重、性别和球员速度的影响。

(4) Write a short report recommending poles for players with different levels.
（4）为不同水平的玩家推荐杆子的简要报告。

Problem B If you spot a lantern fly…
问题 B 如果你看到一只萤火虫…

Spotted lanternflies (Lycorma delicatula) are insects from Asia that are quickly spreading in North America and have a growing negative effect on agricultural production. Since their arrival to the USA about ten years ago, they have now spread to at least 16 states (PA, NY, NJ, MD, MI, OH, IN, WV, VA, NC, DE, CT, RI, MA, KY, TN). These insects are particularly dangerous for grapevines, which is becoming a major concern for many vineyards and wineries present in NY State. Spotted lanternflies feast on plant’s sap and remove so much of it that the vine has far lower chances of surviving the cold temperatures. Even if a seriously affected vine survives, it is much less likely to produce any grapes next season. Quarantine measures in several states and public eradication campaigns have not proven successful in eliminating this threat. Most scientists expect the spread to continue until the lanternflies face off with some natural predators– either those already keeping the lanternfly population limited in Asian countries1 or the native US birds and insects once they recognize the spotted lanternflies as suitable food. Either way, this process will take at least 5-10 years and for now the goal is to slow down the spread (e.g., through quarantine measures) and limit the immediate economic impact (e.g., by treating vines with insecticides).
发现性萤火虫（Lycorma delicatula）是来自亚洲的昆虫，它们在北美洲迅速传播，对农业生产产生了越来越大的负面影响。自从大约十年前它们抵达美国以来，它们现在已经扩散到至少 16 个州（宾夕法尼亚州、纽约州、新泽西州、马里兰州、密歇根州、俄亥俄州、印第安纳州、西弗吉尼亚州、弗吉尼亚州、北卡罗来纳州、特拉华州、康涅狄格州、罗德岛州、马萨诸塞州、肯塔基州、田纳西州）。这些昆虫对葡萄藤尤其危险，这已成为纽约州许多葡萄园和酒庄的主要担忧。发现性萤火虫以植物的汁液为食，吸取了太多的汁液，使得葡萄藤在寒冷的温度下生存的机会大大降低。即使严重受影响的葡萄藤幸存下来，它在下个季节生产葡萄的可能性也大大降低。在几个州的隔离措施和公众根除运动并没有证明在消除这一威胁方面是成功的。大多数科学家预计，直到发现性萤火虫面对一些天敌（无论是在亚洲国家保持萤火虫种群有限的那些天敌，还是一旦它们将发现性萤火虫视为合适的食物，就会将其视为合适食物的本地美国鸟类和昆虫）之前，它们的传播将继续。 无论如何，这个过程至少需要 5-10 年，目前的目标是减缓传播（例如，通过隔离措施）并限制立即的经济影响（例如，通过用杀虫剂处理葡萄藤）。

Your team is asked to address the following two challenge problems.
您的团队被要求解决以下两个挑战性问题。

In addition to your detailed manuscript, please provide a one-page executive summary for the members of the Integrated Pest Management Program . While highlighting your recommendations, please make sure to also address the limitations of your modeling approach and possible directions for future improvement.
此外，请为综合害虫管理计划的成员提供一份一页的执行摘要。在强调您的建议的同时，请确保也讨论您建模方法的局限性以及未来改进的可能方向。

Challenge 1: Limiting the spread in NY State
挑战 1：限制纽约州的传播

Spotted lanternflies (SLF) hatch from eggs & start their life as nymphs in April, become adults by late July, lay their eggs in September-November, and then die in December. Each female SLF usually lays at least one “eggmass” with about 35 eggs in it.
发现性萤火虫（SLF）在 4 月份从卵孵化，以若虫的身份开始生活，到 7 月底成熟，9 月至 11 月产卵，然后在 12 月死亡。每只雌性 SLF 通常至少产下一个含有约 35 个卵的“卵块”。

SLF can feed on more than 100 different plants (which makes it much easier for them to spread), but their all-time favorite is the so-called “Tree of Heaven” (Ailanthus altissima). If it is present in the vicinity, the lanternflies are known to lay about 7 times as many eggs as usual. Thus, removing these trees (present in Ithaca and, more broadly, in the Finger Lakes region) may be one of the most effective anti-SLF measures. But some of the current guidelines recommend using a “tree trap” approach; i.e., removing only small Trees of Heaven while treating the larger ones with a long lasting insecticide (dinotefuran) to kill the returning SLF.
SLF 可以以超过 100 种不同的植物为食（这使得它们更容易传播），但它们最喜欢的还是所谓的“天堂树”（Ailanthus altissima）。如果附近有这种树，已知灯蛾会产下比平时多约 7 倍的卵。因此，移除这些树（存在于伊萨卡以及更广泛的指湖地区）可能是最有效的反 SLF 措施之一。但一些当前的指导方针建议采用“树陷阱”方法；即只移除小型的天堂树，而用长效杀虫剂（dinotefuran）处理较大的树以杀死返回的 SLF。

SLF cannot fly too far on their own – the natural distance they can cover in one year is estimated to be between 4 and 10 miles only. But the spread becomes much faster when they lay the eggmass on shipping materials, railroad cars, or automobiles, which by April, when the eggs hatch, can be in a very different location. Thus, the quarantine measures are usually focused on finding and destroying the eggmasses before they have a chance to travel far.
SLF 无法独自飞得太远——它们一年内能覆盖的自然距离估计只有 4 到 10 英里。但它们在运输材料、火车车厢或汽车上产卵时，传播速度会快得多，到 4 月，当蛋孵化时，它们可能已经到了一个非常不同的地方。因此，隔离措施通常集中在在它们有机会远行之前找到并销毁卵团。

You need to model the SLF population spread in NY State and suggest the best strategy for slowing it down. Regular inspections of vehicles & railroad cars require resources (money, time, coordination with businesses and agencies, human efforts), which could be otherwise spent on other measures – e.g., on reducing the number of Trees of Heaven (TOH) or setting up “tree traps”. Suggest a strategy for balancing these efforts. Explain the predicted effect on the overall SLF population as well as the economic and environmental impact in the next five years.
您需要模拟纽约州 SLF 种群分布，并提出减缓其的最佳策略。对车辆和铁路车辆的定期检查需要资源（资金、时间、与企业和机构的协调、人力），这些资源本可以用于其他措施——例如，减少天堂树（TOH）的数量或建立“树木陷阱”。建议一种平衡这些努力的策略。解释预测对整体 SLF 种群的影响，以及未来五年的经济和环境影响。

Challenge 2: Saving the grapes and/or saving the vines?
挑战 2：保存葡萄还是葡萄藤？

● In the Spring: at least 15-20 nymphs per vine before you spray (one application should be enough).
● 在春季：喷洒前每株葡萄至少有 15-20 个若虫（一次喷洒应该足够）。

● In August-September, when the adult SLF are migrating and many of them move to vineyards: at least 5-10 adult SLF per vine before you spray (repeated applications might be needed).
八九月期间，当成年 SLF 迁徙并且其中许多迁往葡萄园时：喷洒前每棵葡萄至少有 5-10 只成年 SLF（可能需要重复喷洒）。

All insecticides have different effectiveness against the SLF, but also come with different restrictions: on the maximum dose that can be used per year and on the Pre-Harvest Intervals (PHI) – i.e., the number of days that has to pass after the last application before you are allowed to harvest the grapes.
所有杀虫剂对 SLF 的效果不同，但也伴随着不同的限制：每年可使用的最大剂量以及收获前间隔（PHI）——即在允许收获葡萄之前，必须经过的最后一次施用后的天数。

This presents a hard dilemma when the adult lanternflies arrive close to the harvest time.
这在大青虫接近收获时间时，呈现了一个难题。

If you start using insecticides, you will likely have to harvest later than intended, which increases the potential incidence and severity of fungal diseases, resulting in reduced yield as well as reduced grape quality. On the other hand, if you decide to wait with the insecticide until after the harvest, you risk long-term damage to your vines due to SLF sap feeding.
如果您开始使用杀虫剂，您可能会不得不比预期晚收获，这会增加真菌病的潜在发病率和严重程度，导致产量减少以及葡萄质量下降。另一方面，如果您决定在收获后使用杀虫剂，您可能会因 SLF 树液吸取而面临长期损害葡萄的风险。

Suggest an optimal strategy for using insecticides throughout the season. Among other measures, this might involve changing the threshold of observed SLF (nymphs and adults) before you spray or, more generally, making that threshold depend on
建议在整个生长季节使用杀虫剂的优化策略。在其它措施中，这可能包括在喷洒前改变观察到的 SLF（若虫和成虫）的阈值，或者更普遍地，使该阈值取决于

● SLF migration patterns,
● SLF 迁移模式，

● the number of days remaining until the harvest,
剩余天数至收获

● the chemicals already used up to that point, and/or
● 到那时已经用完的化学品，以及/或者

● the predicted weather (which influences the development of fungal diseases).
● 预测的天气（影响真菌病害的发展）。

In addition to financial considerations, please also address a possible impact of your approach on other (beneficial) insects.
除了财务考虑之外，请还考虑您的方法对其他（有益的）昆虫可能产生的影响。

Problem C The Federal Reserve Raises Interest Rates
美联储上调利率

In 2023, the Federal Reserve basically continued the aggressive interest rate hike policy of the previous year, holding a total of 8 monetary policy meetings throughout the year Among them, there were four interest rate hikes in January, March, May, and July meetings, each by 25 basis points. The US federal funds rate reached 5.25% to 5.5%, the highest level in 22 years.
2023 年，美联储基本上延续了前一年的激进加息政策，全年共举行 8 次货币政策会议。其中，1 月、3 月、5 月和 7 月的会议各进行了 25 个基点的加息。美国联邦基金利率达到 5.25%至 5.5%，为 22 年来的最高水平。

The Federal Reserve's aggressive interest rate hikes continue to disrupt the world economy. First, the aggressive interest rate increase policy has led to the soaring yield of long-term U.S. treasury bond bonds, increased the cost of auto loans, credit card lending and various forms of commercial loans, raised the cost of living of U.S. residents, and severely squeezed small and medium-sized banks from the asset side and the liability side, leading to financial risks; Secondly, the aggressive interest rate hike policy has generated strong spillover effects. It has driven the strengthening of the US dollar, prompted international capital to flow massively from emerging markets to the United States in pursuit of higher returns, continuously compressed the monetary policy space of other economies, and forced many countries to make more difficult choices between cross-border capital flows, monetary policy independence, and exchange rate stability; Thirdly, aggressive interest rate hikes have increased the debt servicing costs of emerging markets and developing economies, leading to currency weakness in some economies, making their economic growth prospects even more bleak, exacerbating global financial market turbulence, and hindering the recovery process of the world economy.
美联储的激进加息持续扰乱世界经济。首先，激进加息政策导致长期美国国债收益率飙升，增加了汽车贷款、信用卡贷款和各种形式的商业贷款的成本，提高了美国居民的生活成本，并从资产和负债两方面严重挤压了中小银行，导致金融风险；其次，激进加息政策产生了强烈的溢出效应。 它推动了美元的强化，促使国际资本大量从新兴市场流向美国以追求更高的回报，持续压缩其他经济体的货币政策空间，迫使许多国家在跨境资本流动、货币政策独立性和汇率稳定之间做出更艰难的选择；其次，激进的加息增加了新兴市场和发达经济体的债务服务成本，导致某些经济体货币疲软，使它们的增长前景更加黯淡，加剧了全球金融市场动荡，阻碍了世界经济的复苏进程。

At the monetary policy meeting in December 2023, the Federal Reserve announced that the target range for the federal funds rate would remain unchanged between 5.25% and 5.5%. Federal Reserve Chairman Powell said at a press conference after the meeting that the current federal funds rate "may be close to the peak of this tightening cycle," and attending Fed officials generally believe that "further interest rate hikes are unlikely to be appropriate," but they also do not want to rule out this possibility.
在 2023 年 12 月的货币政策会议上，美联储宣布联邦基金利率的目标区间将维持在 5.25%至 5.5%之间不变。美联储主席鲍威尔在会议后的新闻发布会上表示，当前的联邦基金利率“可能接近这一紧缩周期的峰值”，出席美联储的官员普遍认为“进一步加息可能不合适”，但他们也不愿排除这种可能性。

Analysts believe that it is not easy for the Federal Reserve to control a reasonable shift in monetary policy. On the one hand, the Federal Reserve still faces the "last mile" challenge of combating inflation; On the other hand, it is necessary to ensure the flexibility of monetary policy and avoid overcorrection. During the policy shift, it may also have an impact on the global financial market and bring more uncertainty to the world economy.
分析师认为，美联储控制货币政策合理转变并不容易。一方面，美联储仍面临抗击通胀的“最后一公里”挑战；另一方面，确保货币政策的灵活性并避免过度纠正也是必要的。在政策转变期间，也可能对全球金融市场产生影响，给世界经济带来更多不确定性。

In September 2024, the Federal Reserve unexpectedly announced a rate cut, causing global capital markets to flock to the Chinese stock market. In early October, the unexpected non farm payroll data released by the United States once again left the market confused. Will the Federal Reserve raise interest rates again? Can the Chinese market continue to attract global capital? How will the future of the global market go?
2024 年 9 月，美联储意外宣布降息，导致全球资本市场纷纷涌入中国股市。10 月初，美国意外发布的非农就业数据再次让市场陷入混乱。美联储是否会再次加息？中国股市能否继续吸引全球资本？全球市场的未来将走向何方？

Consider the background information and address the following:
考虑背景信息，并解决以下问题：

(1) In history, the Federal Reserve has adopted strategies of raising or lowering interest rates at different times. Please choose appropriate indicators, collect data, establish a model to predict the Fed's strategy of raising or lowering interest rates, and discuss the effectiveness and accuracy of the model;
(1) 在历史上，美联储在不同时间采取了提高或降低利率的策略。请选择合适的指标，收集数据，建立模型以预测美联储提高或降低利率的策略，并讨论模型的有效性和准确性；

(2) Please establish a model to analyze the monetary policy that China will adopt when the Federal Reserve implements a rate hike or cut strategy. And what kind of impact will the policies adopted by China have on the national economy. Among them, please choose appropriate indicators to characterize the specific impact.
(2) 请建立一个模型来分析当美联储实施加息或降息策略时，中国将采取的货币政策。以及中国采取的政策将对国民经济产生何种影响。其中，请选择适当的指标来描述具体影响。

(3) Please establish a model to describe the impact of the Federal Reserve's interest rate hike or rate cut strategy on the world economy after a period of time (such as one year)? What strategies should major economies (such as the European Union, ASEAN, Japan, and South Korea) adopt to overcome this impact? What is the impact on the economy?
（3）请建立模型描述美联储在一段时间（如一年）后加息或降息策略对世界经济的影响。主要经济体（如欧盟、东盟、日本和韩国）应采取哪些策略来克服这种影响？对经济有何影响？

Problem D Scheduling and Path Optimization for Autonomous Cleaning Vehicles on Campus
问题 D：校园中自主清洁车辆的调度和路径优化

As campus sizes continue to expand, the challenges of environmental sanitation management have become increasingly prominent. Traditional manual cleaning methods are not only inefficient but also susceptible to factors such as weather and personnel arrangements, making it difficult to maintain cleanliness on campus. To address this issue, many universities have started to adopt smart technologies, with autonomous cleaning vehicles emerging as a new cleaning tool that is gradually gaining attention.
随着校园规模的不断扩大，环境卫生管理面临的挑战日益突出。传统的手工清洁方法不仅效率低下，而且容易受到天气和人员安排等因素的影响，使得在校园内保持清洁变得困难。为了解决这个问题，许多大学已经开始采用智能技术，自主清洁车辆作为一种新的清洁工具，正逐渐受到关注。

These autonomous cleaning vehicles utilize advanced sensors and navigation systems to automatically identify cleaning areas, avoid obstacles, and plan their routes, thereby efficiently completing cleaning tasks. Their advantages include 24/7 operation, reduced labor costs, and improved cleaning efficiency. However, effectively scheduling multiple autonomous cleaning vehicles and reasonably planning their cleaning paths to meet the cleanliness needs of different campus areas at various times remains a pressing challenge.
这些自主清洁车辆利用先进的传感器和导航系统自动识别清洁区域、避开障碍物并规划路线，从而高效完成清洁任务。它们的优点包括 24 小时不间断运行、降低劳动力成本和提高清洁效率。然而，有效地调度多辆自主清洁车辆并合理规划它们的清洁路径以满足不同校园区域在不同时间的清洁需求仍然是一个紧迫的挑战。

In this context, establishing a mathematical model to optimize the scheduling and path planning of autonomous cleaning vehicles is particularly important. Through scientific task allocation and path optimization, it is possible to enhance the operational efficiency of the cleaning vehicles, reduce operational costs, and address challenges posed by unforeseen events. Ultimately, the goal is to achieve intelligent management of the campus environment, creating a cleaner and more comfortable learning and living space for students and faculty.
在此背景下，建立数学模型以优化自主清洁车辆的调度和路径规划尤为重要。通过科学的任务分配和路径优化，可以提升清洁车辆的运营效率，降低运营成本，并应对意外事件带来的挑战。最终目标是实现校园环境的智能化管理，为学生和教职工创造更清洁、更舒适的学习和生活空间。

Chongqing University’s Huxi Campus plans to introduce autonomous cleaning vehicles to improve the efficiency of environmental sanitation management. A mathematical model needs to be established to optimize the scheduling and routes of these cleaning vehicles.
重庆大学虎溪校区计划引入自主清洁车辆以提高环境卫生管理的效率。需要建立一个数学模型来优化这些清洁车辆的调度和路线。

https://mp.weixin.qq.com/s?__biz=MzA5MTU2MTcwNw==&mid=2653094179&idx=1&sn=171c9163a8752d09b9643a364c6607ad&chksm=8a7a1059e21f1fd4b748366d16437c462757f34667cbf80f7b29567ccae08bbaf75a5c67e537&mpshare=1&scene=23&srcid=1018Cqr4OZ2Y60g57pqZIQaa&sharer_shareinfo=4e26de04df6b5d416d5b7c5a62c70ca7&sharer_shareinfo_first=4e26de04df6b5d416d5b7c5a62c70ca7#rd

(1) The campus needs to be divided into multiple cleaning areas to facilitate task allocation for autonomous cleaning vehicles.
(1) 校园需要划分为多个清洁区域，以便为自主清洁车辆分配任务。

(2) A task allocation model should be developed based on the cleaning areas to optimize the efficiency and time utilization of the cleaning vehicles.
(2) 应根据清洁区域开发一个任务分配模型，以优化清洁车辆的效率和时间利用率。

(3) An algorithm must be designed to plan efficient routes for the autonomous cleaning vehicles to cover all designated cleaning areas.
（3）必须设计一个算法来规划自主清洁车辆高效覆盖所有指定清洁区域的路线。

(4) A dynamic scheduling algorithm should be designed to address the impact of unforeseen events (such as activities and weather changes) on cleaning tasks within the campus.
（4）应设计一种动态调度算法，以应对不可预见事件（如活动和天气变化）对校园内清洁任务的影响。

(5) A mathematical model needs to be established to evaluate the operational costs and cleaning effectiveness of autonomous cleaning vehicles to determine their overall benefits in campus management.
（5）需要建立一个数学模型来评估自主清洁车辆的运营成本和清洁效果，以确定其在校园管理中的整体效益。

Problem E Optimal urban population size and employment structure
问题 E 优化城市人口规模和就业结构

With the continuous advancement of urbanization, the urban population size is getting larger and larger, and the survival and development of the urban population are facing many challenges, including survival needs, housing needs, education needs, medical needs, employment needs, public service needs, entertainment needs, etc.
随着城市化进程的不断推进，城市人口规模越来越大，城市人口的生存和发展面临着许多挑战，包括生存需求、住房需求、教育需求、医疗需求、就业需求、公共服务需求、娱乐需求等。

In order to meet the various needs of the urban population, a large amount of resources need to be invested, especially a large amount of human resources are needed, so that the development of the urban population also provides more diversified employment opportunities for the society, forming the employment structure of the population in various industries.
为了满足城市人口的各种需求，需要投入大量资源，尤其是需要大量人力资源，以便城市人口的发展也能为社会提供更多元化的就业机会，形成各行业人口就业结构。

Assuming that the urban population are all active and hardworking workers, with professional knowledge and skills in the required industries, they are efficient production labor after their survival and development needs are met.
假设城市人口都是活跃且勤奋的工人，具备所需行业的专业知识和技能，在满足生存和发展需求后，他们成为高效的生产劳动力。

In order to determine the relationship between urban population size and employment structure, please establish mathematical models and answer the following questions:
为了确定城市人口规模与就业结构之间的关系，请建立数学模型并回答以下问题：

(1) Establish a mathematical model to describe the relationship between urban population size and population demand, and determine the quantitative relationship between urban population size and various demands;
(1) 建立一个数学模型来描述城市人口规模与人口需求之间的关系，并确定城市人口规模与各种需求之间的定量关系；

(2) Establish a mathematical model to describe the relationship between the number of practitioners and the number of products and services they provide, and determine the mathematical model of the number of employed people in each industry;
(2) 建立一个数学模型来描述从业者数量与他们提供的产品和服务数量之间的关系，并确定每个行业的就业人数数学模型

(3) Based on the urban population quantity model and population employment model established in (1) and (2), describe the distribution pattern of urban population among various industries;
(3) 基于第(1)和(2)中建立的城镇人口数量模型和人口就业模型，描述城镇人口在各产业间的分布模式；

(4) Based on the model established in (3), find the optimal urban size;
(4) 基于第(3)部分建立的模型，找到最佳城市规模；

(5) Based on the model established in (4), find the optimal population employment structure.
(5) 基于第(4)部分建立的模型，找到最佳人口就业结构。