Optimization Calculus 1 - 2 Problems

- Okay. So, what we're gonna do today is we're gonna talk about a concept called optimization. Optimization is using the idea of extrema, finding relative or local maximums or minimums to solve real world problems, meaning we're gonna try to maximize or minimize, optimize certain things. So if I was gonna build a deck, I wouldn't wanna buy too much material, 'cause then I'd waste money.  I don't wanna spend or buy too little material because then I wouldn't be able to finish my deck. I want to optimize my checking account and my paychecks so that I can afford what I need and do exactly what I'm looking for. I want to get from one place to another without wasting gas. So I don't wanna spend too much money on gas. I wanna be able to make sure I get just the right amount. If I'm trying to feed or let's say pay employees, what would be the greatest equation or best way to maximize my profits but minimize my costs. I don't want to have to overspend my employees and then never making anything from it. Or what happens if I'm spending for food? I want to buy food for a party. Well, I don't wanna overbuy and have all this wasted food and I definitely don't wanna underbuy because then I wouldn't be a good host and we wouldn't have enough food for the party. So, what we're gonna look at is the idea that we tend to figure out the ideas of optimization, maximums and minimums just in real world life and how we can use calculus to find the same things. So, the first thing that we're gonna talk about is the steps. There are some pretty cookie cutter steps on how to do optimization. So it's not like related rates. Related rates we were changing with respect to time and it varied depending on the type of question we had. Optimization is a lot more straightforward. There's really just three steps we've...