 Let's review the main ideas of section 3.4 in active calculus on applied optimization. There really are no new ideas in this section, instead what we're going to be doing is taking the methods we've learned in section 3.1 and 3.3 for optimization in general, and put them into practice on real world problems where the high and low points of a function could be useful. So this video is not going to be long, instead we have several examples coming up in subsequent videos that you should study very carefully and master the techniques. For now you should just understand two things. First, organization is key for solving optimization problems. You cannot successfully solve most real world problems without spending time understanding the problem and setting up the solution first, diving straight into a calculation from the very beginning almost never works. You should start every optimization problem by asking the following. What is the quantity in this problem I'm being asked to optimize? Second, what do I know about this quantity? Is there a formula that specifies it? Is there enough information in the problem to set up such a formula and so on? Third, how does the target quantity that I'm trying to optimize relate to the other quantities in this problem? And can I write an expression that makes that relationship formal? And most importantly, can I express the target quantity that I want to optimize in terms of exactly one of the other variables in the problem? This is really crucial. All optimization problems turn on being able to make your target quantity, that is the quantity you wish to maximize or minimize, a function of one and only one input variable. So in step three, you might have come up with a relationship between your target quantity and the other quantities that involves several variables. Now you need to do whatever mathematics it takes to get this down to a function of one of those other variables. Second, organizing a solution involves careful representation of the problem. You will need to draw pictures, make tables of data, take examples of the problem, and so on before a general solution will really come to you. You need to expect this to take time and a little bit of failure at first. But the more success you have at it in the end, the better you will get at it. Now let's look at a few examples of applied optimization.