# Calculus Final Project Spotlight: Packaging Consultants

*And the last project I am going to detail…*

A few students did a pretty standard, but well done optimization project **investigating different can shapes to find which one is the most efficient** *(Sam profiled his kids doing a very similar project, I loved reading his students’ reflections on it!)*. Then they redesigned the cans to help companies lower cost. The reason that I am profiling this because it made me realize what students find interesting in this whole optimization nonsense – I brought in cans in the winter when we first learned optimization, and we did something similar, but we never talked about the issue that really got other students’ attention…. **money!** I had been focusing on the shapes, but I should have been focusing on **money!** *(Seems like a super “duh” in retrospect, and it’s not anything original, but helpful to realize nonetheless).*

The students did tons and tons of calculations, but what I really loved is that they compared the **price of producing the current can that the company produces and the price of producing the ideal can**. They looked up the price of aluminum and estimated (or looked up? I’m not sure here) how many cans per day a factory would produce. After a bunch of multiplication, they showed that tiny, tiny changes in the shape would result in savings in the hundreds of thousands of dollars range for a year (see red number below), which is super cool.

Also, they had a really nice framework for their project. They pretended they were a packaging consulting company and even came up with a logo and a name that combined their names. I thought that was great!

**NEXT YEAR:** I am going to frame my optimization unit much more in the way these students went about it. I feel like this is a complicated mini experiment in terms of #anyqs – the students found for me what the actual interesting question is. For me, the shapes of the cans themselves is interesting (especially that it ends up being such a beautiful ratio), but I think a lot of kids were really amazed at how a small change in the size of the cans can result in huge savings and led them to wonder why all cans aren’t shaped the same way. So, thanks for helping improve my curriculum, (now former) students!

Posted on June 4, 2012, in Calculus, End of the year projects and tagged Calculus, cans, consulting, cylinders, optimization. Bookmark the permalink. 2 Comments.

It would be even cooler if they did it with a real can of something and wrote to the company with their results.

yeah totally! they DID do it with a real can, so that would have been really cool to take that one extra step of writing a letter. definitely will do that next year.