Part 1: Optimization is a term we use a lot in calculus, but what does it mean? Define optimization, tell what it means. Then, talk about how we can use calculus to find the optimization. And finally, find a real world example of where optimization is used. Don't forget to site your sources and be detailed in your explanation. Please don't give a generic answer but give a well researched answer.

Part 2: We are going to optimize the volume of the box below without a lid. You just need to choose a value for \( a \) and \( b \). So, define both \( a \), and \( b \), but make sure that they are between 2 and 20 .