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Optimization Problem #4 - Max Area Enclosed by Rectangular Fence

Maximizing the Area of Rectangular Fence

Using Calculus / Derivatives.

In this video, I show how a farmer can find the maximum area of a rectangular pen that he can construct given 500 feet of fencing. We can actually solve this quite easily using algebra but here I am trying to show the overall process that we use on maximization / minimization problems.

I find the maximum volume of a box made from a 2ft x 2ft piece of metal when corners of equal size are removed and then the sides of the box are folded up.

In this video, we have a certain amount of material with which to make a cylindrical can. We have to find the radius and height that would maximize the volume of the can.

In this video, we take a piece of wire, cut it into two piece (not necessarily equal!) and form those pieces into two squares. What is the minimum area enclosed by the the two squares?

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