I get lots of questions about Section 2. Many of the questions come from students who have not watched all (or sometimes *any*) of the lecture videos first. Note that you need to watch ALL of the Section 2 movies before you begin work on ANY of the Section 2 homework assignments. Don't try to shortcut this process or you'll end up wasting a lot of time being confused. Also, if you are still thinking that you'll "just read the book" or "just figure it out" now is the time to realize that this isn't going to work for you. The movies include lots of hints and tips that simply aren't available anywhere else. So my first bit of advice is: Watch all six of the Section 2 movies before you start the homework on Section 2.
Another thing students commonly ask is "Can you just give me a 'to do' list for these types of problems?". Sure. And here it is:
(1) If it is a word problem, write the inequalities and the function. If the inequalities and function are given, skip this step.
(2) Graph all of the inequalities. You can do this by hand, with a graphing calculator (if you have one that you've used in previous classes), or using any kind of equation grapher that you might find online. How you graph is totally up to you. (Since graphing is something that you should have learned well in earlier math courses, the lectures do not cover how you should do this. You'll need to review this information or ask me for assistance if you've totally forgotten.) Once you graph, note that you will NOT be using this graph to find your answers. It is just used as a "rough idea of what is going on". So getting a graph that gives you a general idea of how and where these particular lines cross each other and where they cross the x- and y-axes is all you are really looking for.
(3) Find the solution region. You do this using the "plug in the point (0,0)" method described in the movies. Then determine where all the solution regions overlap one another at the same time. That is your solution region.
(4) Determine the corner points. These are the "joints" that directly touch your solution region. (There are lots of "joints" on the graph, but only the ones that directly touch your solution region are considered corner points. You never need to find points that don't touch your solution region.) You'll be able to spot the corner points on your graph, but to find the exact coordinates of a particular point you'll use the row operation tool (as described in the movie on this topic). Just figure out which two lines cross at the point you are interested in, put those 2 lines into the tool, and find the exact point where the two lines cross. You have to repeat this for each point you want to find. Note: The equation of the x-axis is y=0. The equation of the y-axis is x=0.
(5) (If required) To find the point that maximizes or minimizes the function, plug in each of the corner points into the function and see which one gives you the highest/lowest value.
Yes, these take time. However, once you do a few of them you'll start to see that they are all very similar to one another and the process is very much the same from one problem to the next - even if the graphs look totally different. Take the time to do things correctly and it will really pay off in the end. I promise!
Note: Remember that you will only have 3 submissions per answer blank on the test. So if the methods you are using to get the answers to these types of problems are taking more than 3 submissions you need to really figure out what you need to do to make sure you are getting the right answers on the first submission (or at least by the third submission!). Guessing on these might eventually get you good grades on your homework, but you'll really be hurting your test grade, which is worth a lot more in the end.