IB Mathematics HL IA (19/20)

Research Topic : Comparison of water bottles in terms of economic and environmental efficiency by calculating surface area of water bottles using Calculus

Introduction

For the last 7 months, I had a chance to enter the Entrepreneurs of Tomorrow (Business plan competition) run by American German business club in Frankfurt. In order to make a good business plan, not only I had to think of an appropriate goods and services to provide, industry investigation, marketing and sales strategy, but I also tried to minimize the costs of factors of production. All these elements were to be well considered in order to make the company to make profits, but I was especially interested in minimizing the costs of goods I am producing. 1A book called “Restaurant success by numbers” by Roger Fields explains how much difference it would bring if a restaurant lower costs by 1 dollar to make pasta. It actually has a serious link to efficiency of the restaurant, which could potentially bring about a greater profit. I was fascinated about the fact that even though 1 dollar does not seem to be a great amount of money to deal with, it has a great link to success of the business once you eliminate that 1 dollar from the cost. Therefore, I was interested in comparing which firms are being most efficient in terms of its costs of production.

When I was brainstorming which products I should compare in terms of efficiency, it came up to my mind that it would be great if I could link some environmental factors in as well. After contemplating many types of products involving some environmental issues, I ended up with a plastic water bottle. As everyone is aware of, plastic causes serious environmental problems. When left in the nature, it takes 450 years for a plastic bottle to decompose. Some plastic wastes are just left in the ocean, killing a significant number of marine life. Therefore it would be meaningful to compare use of plastic to make a plastic water bottle by company so that we are aware of which company is more eco-friendly, producing less plastic waste and being more efficient.

I chose to compare efficiency of 2 plastic water bottles with volume of 500ml from different companies. Efficiency will be investigated according to the surface area of each water bottle, which will give me a general idea how much of plastic was used to make the bottle. Surface area will be calculated mathematically. My plan is to find the closest function that describes the side of the water bottle using a computer program and from that, I will be able to find its surface area using calculus…