Folding a wire into the largest rectangle | Optimization example

Suppose you have a wire of length L. The goal is to fold it into a rectangle. What choices give the largest possible area of the rectangle? This classic optimization problem involves a constraint and an optimizing equation where we use the constraint to find a function of only a single variable. Then, we can take the derivative to find the critical point and test that it truly is a maximum.

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Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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[helllv]

Aa if our only C.P. is the maximum one... how can we determine the minimum area?

[rustedcheese]

How do we do this exact thing but excluding one side. Imagine someone has 300m of fencing but he is allowed to use the boundary fence of his property.

[franciscopen]

Regarding the end points, if x approaches 0, then wouldn’t Y approach infinity? You said A=x*y, so 0 times ♾ that is an indefinite form. You disregarded it as 0, and because Y is defined as a proportion, shouldn’t we analyze also that?