Now we put our optimization skills to work.

In this section, we will present several worked examples of optimization problems. Our method for solving these problems is essentially the following:
Draw a picture.
If possible, draw a schematic picture with all the relevant information.
Determine your goal.
We need to identify the quantity that needs to be optimized.
Find constraints.
What limitations are set on our optimization?
Solve for a single variable.
Now you should have a function to optimize.
Use calculus to find the extreme values.
Be sure to check your answer!

We now work a similar problem without concrete numbers.

With optimization problems you will see a variety of situations that require you to combine problem solving skills with calculus. Focus on the process. One must learn how to form equations from situations that can be manipulated into what you need. Forget memorizing how to do “this kind of problem” as opposed to “that kind of problem.”

Learning a process will benefit one far more than memorizing a specific technique.