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본 문서는 IB M22 Math AA HL IA입니다. 총점 18/20를 받아 7점을 프리딕을 받았고 최종점수 역시 7점 받았습니다.



1. Introduction

From the news, social media, and school, I’ve always known that single-use plastic products, with plastic bottles taking up a large portion, is a growing environmental burden, releasing toxins and harming wildlife. While these spillover effects concern me, I find myself continuing to use plastic bottles due to the convenience and situations where no alternatives are available. This makes me feel guilty each time I go to the store to buy plastic bottles. After countless guilty trips to the store, I started to notice the wide variety of brands that have each packaged their water differently; some bottles were taller, wider, or curvier. I wondered why these bottles were designed so differently, and if certain designs alleviated environmental burdens more than others. Assuming the thickness of the bottle to be constant, such bottle would have the smallest surface area, indicating least amount plastic used, for the same volume capacity. Therefore this investigation aimed to find ways to modify preexisting dimensions of plastic bottles to minimize surface area of bottle. For this purpose, I focused on optimizing a 550ml Nongfu Spring plastic water bottle, which is the bottled water I usually purchase.

For redesigning the bottle, some realistic constraints were considered. If all brands were to produce their bottles using the same optimized design and dimension, the brand identity would be diminished as all bottles would look identical and none would stands out. Additionally, if the optimized bottle were to have excessive capacity, the water bottle would be heavy, and if the dimensions for the bottle neck were to be altered, the precision and rate of water flowing out would be at a level unfamiliar to consumers. These factors degrade utility, affecting the desirability of that bottle. In these cases, companies would be unwilling to produce plastic bottles with optimized surface area to volume ratio, resulting the redesigned bottle to be inapplicable. Hence when considering the economic factors in addition to environmental factors in redesigning the bottle, the general design used to differentiate brands and factors of utility, including volume capacity per bottle and dimension of bottle neck, shouldn’t be altered. The numbers in this paper were rounded to the fifth decimal place for readability, but the calculations were carried out with unrounded numbers…


  • 총 페이지수: 17 pages
  • 과목명: Mathematics
  • 주제: IB M22 Math AA HL IA
  • The file is in PDF format.
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