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Quadratic Equation Word Problem : Maximum Area - Six Cages With a Chain Link Fence

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1500 feet of chain link is to be used to construct 6 animal cages as shown below. Find the maximum value of this area and the dimensions that yield this area.

The area is a rectangle were the side is x. The bottom is y. It is divided by dotted lines into 6 squares where the bottom and sides are x.

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Area is maximized with a quadratic equation. The solution is detailed and well presented.

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First let me point out there are many ways to solve an optimization problem. You could use linear programming, nonlinear programming, the lagrange method, etc. In all these problems you have an objective function that you are trying to maximize and a constraint. In your case you are trying to maximize area subject to the constraint that the total fence length is less than 1500 feet.

First you have a long side that is length y and a short side that is length x. ...

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