Optimization in problem solving and studying

In summary, optimization is a problem-solving technique used to find the maximum or minimum value of a given quantity. It is commonly used in math problems to find the maximum volume, minimum distance, or minimum length. The key to solving optimization problems is to find a way to relate the unknown variables in a way that maximizes or minimizes the given quantity. It is not a set process and can involve using equations to find the optimal solution. Optimization can also be used to find the maximum area of a square fence with a given amount of fencing.
  • #1
SpicyRamen
40
0
This might be a stupid question, I'm not use to asking questions about math...

I just started on optimization. Can someone tell me What optimization is used for and how I could apply it to a problem. When it comes to a problem, I could do it like if it asks " Find two numbers that satisfy the given requirements,' The sum of (S) and the product is maximum.'" Like when They ask me that I can definitely do that no problem, but my teacher usually gets us with blinding questions that I have never seen before in our books, I know he's only trying to prepare us for the Ap exam, but sometimes No matter how much I study from the book I just don't know how to prepare for the test. He teaches us the material and I'm all like "Hey I totally get how to do this" But during the test he gives us problems we have never seen before and wants us to apply what we learn, so I want to prepare for the worst. I want to know why optimization is used. I know it's used to find max volume, minimum distance and area and min length, But why? Can someone give me a definition of optimization or show me using an equation how it originates.
 
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  • #2
There's no set way to do optimization problems. Really the only things that all the problems have in common is that to solve you need to find a way to relate the unknown quantities that will maximize/minimize another given quantity. It's used just as is says to optimize. If you can relate a unknown quantity(s) in a way which maxs/mins the given quantity.

Say we're maximizing a fence, you've got 200 ft of fence and you're asked to maximize the area. Basically you go through a process find a way to relate the variables (x and y would be used here i guess) to the area. If you maximize the function relating the sides of the fence to the area then you get the dimensions (of the fence in x and y) which would make the area the largest it can ever be with the given constraints.
 
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  • #3
So for the problem you gave me

I would write-

A= x+y
200= xy

y=200/x

A=x+(200/x)
=1-(200/x^2)
X= (200)^(.5)
= 10*(2)^.5

Y= 10*(2)^.5

Is x and y always the same? And when we're finding the max volume is the base always square(Shape)? Is optimization only used to find the max volume, is there a min volume?
 
  • #4
Area=length x width=x*y
Parameter=2x+2y=200

In the case of a fence you'd maximize the are if you made a square fence so you can fairly easily see that the maximum area is 2500 ft^2 with each side being 50 feet.
 

Q: What is optimization in problem solving and studying?

Optimization in problem solving and studying is the process of finding the best possible solution to a given problem or task. It involves identifying and implementing various strategies and techniques to maximize efficiency and effectiveness.

Q: Why is optimization important in problem solving and studying?

Optimization is important because it allows us to solve problems and complete tasks more efficiently and effectively. By optimizing our approach, we can save time, resources, and effort, and ultimately achieve better results.

Q: What are some common techniques for optimization?

There are several common techniques for optimization, including breaking down a problem into smaller, more manageable parts, using trial and error to test different solutions, and applying analytical and logical thinking. Other techniques include seeking outside perspectives and feedback, setting clear goals and priorities, and using technology and tools to aid in the problem solving process.

Q: How can I apply optimization in my own problem solving and studying?

To apply optimization in your own problem solving and studying, start by identifying the main goal or objective of the task at hand. Then, break down the problem into smaller parts and consider different strategies and techniques that could be used to solve each part. Experiment with different approaches and evaluate their effectiveness. Seek feedback and outside perspectives, and make adjustments as needed to optimize your process.

Q: Are there any potential challenges or limitations to optimization in problem solving and studying?

While optimization can be a helpful tool in problem solving and studying, it is important to recognize that it may not always be the most appropriate approach. Some challenges or limitations of optimization include the possibility of overlooking important factors or solutions, becoming too focused on efficiency rather than effectiveness, and the potential for bias or subjectivity in decision making. It is important to consider the specific context and goals of the problem at hand before applying optimization techniques.

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