Problem A: The Need for Bees (and not just for honey)

Honeybees, along with a few other key animals, are critical to human existence on our planet. Along with honey production, these insects provide the vital role of pollination of many trees and plants that provide food for our survival. In 2007, the term Colony Collapse Disorder (CCD) was created to describe the decline of honeybee populations around the world. Bee decline can be attributed to factors such as viruses, pesticides, predators, habitat destruction, and environmental conditions.

Some information to consider (but you may find other helpful information online):

Honeybees can travel up to 20 km, but typically stay within 6 km of their hive.

A typical honeybee hive contains between 20,000 and 80,000 honeybees.

A single honeybee can visit approximately 2,000 flowers or more in a single day.

Because of the high workload during summertime, most honeybees work themselves to death, resulting in a shorter lifespan.

During autumn and wintertime, honeybees may live a bit longer (four to six months).

A honeybee’s level of activity, pollen consumption, and protein abundance impacts its lifespan.

Requirements

Develop a model to determine the population of a honeybee colony over time.

Conduct sensitivity analysis on your model to determine which factors (e.g., lifespans, egg laying rates, fertilized/unfertilized egg ratios, or other factors) have the greatest impact on honeybee colony size.

Model and predict how many honeybee hives you will need to support pollination of a 20-acre (81,000 square meters) parcel of land containing crops that benefit from pollination.

Create a non-technical, one-page blog or infographic for a website that provides the information you developed.

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

One-page Summary Sheet.

Table of Contents.

Your complete solution.

One-page blog or infographic.

References list.

Note: TheMCM Contest has a 25-page limit to your PDF solution submission. All aspects of your submission count toward the 25-page limit (Summary Sheet, Table of Contents, Reference List, and any Appendices).

问题 A: 蜜蜂的需求（不仅是蜂蜜）

蜜蜂和其他一些重要动物对人类在地球上的生存至关重要。随着蜂蜜的生产，这些昆虫为许多树木和植物提供了重要的授粉作用，为我们的生存提供了食物。2007年，“蜂群衰竭失调”（CCD）一词被创造出来，用来描述世界各地蜜蜂数量的下降。蜜蜂数量下降可归因于病毒、杀虫剂、捕食者、栖息地破坏和环境条件等因素。

需要考虑的一些信息（但您可以在网上找到其他有用的信息）：

蜜蜂可以移动20公里，但通常停留在距离蜂巢6公里的范围内。

一个典型的蜂箱包含20，000到80，000只蜜蜂。

一只蜜蜂可以在一天内拜访大约2000朵或