What steps do I need to take when dealing with optimization? I don't have an exact question in mind, however every time I am faced with one I don't know where to begin. If someone could just give me general steps to figuring out these questions I would highly appreciate it. 
An example question would be: Find the dimensions of the rectangle of maximum area that can be formed from a 370-in. piece of wire.
The answers is in in^2, if that changes anything. 
Thank you for your time !
 A: See what we know. We know that $2(x+y)=370 \text{  (The perimeter)}$. 
$$A(x,y)=xy$$
Where $A$ is the area function. But we already know $y$!! So we can change it in terms of some number and $x$, so we get $y=185-x$. 
Substituting, we get $A(x)=x(185-x)$. 
And this is what you wanted.
As far as the answer is concerned, differentiation and equating to $0$ gives, $$185-2x=0$$ and hence $\frac{185}{2}=x$ and $y=\frac{185}{2}$. So this can be generalized to, "A rectangle with a given perimeter of maximum area will be a square." And also, this cannot be the minimum, because $0$ will be the minimum and a quadratic function cannot have more than one critical point. Hence, we found the maximum!

Your reasoning and analytic approach would definitely help you. But first you should note down the things you know. (Which are constant), like in this example, we knew a fixed perimeter for variable $x$ and $y$. 
Now formulate a function in $x$ and $y$, and substitute the value of $y$ in terms of $x$, from the previous condition.
A: The general steps would be to realize what they give us, and what they're asking for. 
You would 
1. Find the derivative of the formula you need to use (such as if you're looking for area).
2. Solve system of equations for one variable.
3. Plug in for that variable in the original formula (not the derivative)
4. This should give you everything in one variable, so you can find the answer to one variable and plug in for the next.
