IB Internal Assessment Investigating the most optimal packaging for makeup products
You must adhere to not using any plagiarism or artificial intelligence.
The question is ″Investigating the most optimal packaging for makeup products. ″ The assessment is split into five categories: A, B, C, D, and E. Personal Engagement, Mathematical Exploration, Reflection, and Communication. The limit is 12 to 20 pages.
Assessment Layout
The assessment layout is as follows:
- Introduction and rationale
A brief story of why I chose this question- I am interested in Makeup and the environment/minimizing waste products
-Background information
What do you/the reader need to know to understand (prior knowledge) what you will be talking about? Briefly explain why packaging optimization is important in the cosmetics industry, touching on factors like cost efficiency, environmental impact, and consumer appeal.
-Objective/Aim
What are you doing, how are you doing it, what do you expect to find?
- Methodology
What did you do, and how did you do it? Add some data Calculations:
THERE WILL BE 3 PRODUCTS INVESTIGATED.
All calculations are here. Discuss all the calculations, mean, tables that must be referenced, and variables that must be defined.
- Liquid foundation of your choosing, add the brand name (Rectangular prism).
Packaging Type: Rectangular bottle with a pump or a squeeze tube.
Reason: The foundation’s packaging is often bulky to accommodate pumps, making it an interesting subject for reducing wasted space.
- Setting spray (Cylindrical spray bottle)
- Eyeshadow Pallete (Flat rectangular prism).
Assumptions:
List any assumptions you are making (e.g., the volume of the product remains constant, packaging must protect the product from damage, etc.).
Mathematical Concepts:
Use concepts such as surface area, volume, optimization, and constraint equations.
Discuss any geometric shapes that approximate the packaging (e.g., cylindrical for setting spray, rectangular prism for a foundation bottle).
Formulation:
Set up mathematical models to represent the packaging. This could involve deriving formulas for the surface area of each product′s packaging and then finding the minimum surface area required for the given volume.
Existing Packaging: Analyze the current packaging’s surface area and volume. This will provide a baseline for comparison.
Comparison: Calculate the total wasted space by comparing the current packaging′s surface area with the optimal surface area you’ve calculated.
Implications: Discuss the implications of your findings. How much material can be saved? What are the potential cost savings? How does this impact environmental sustainability? Include limitations
Summary: Summarize the main findings of your investigation. State whether your research question was answered.
Final Thoughts: Reflect on the importance of packaging optimization and how your findings could be applied in real-world contexts.
Personal Engagement: Reflect on your learning process. Discuss what you found challenging, what you learned, and how this investigation has impacted your understanding of both mathematics and its applications.