optimization word problem

A

aldricj

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Feb 2, 2011
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Not sure how to even go about doing this problem. A rectangular banner has a red border and a white center. The banner has an 8 inch border at the top and the bottom, and it has a 6 inch border on each side. The total area of the banner is 27 ft squared or 3888 in squared. What should be the dimensions of the banner (x and y) if the area of the white center is to be a maximum? If possible, it would be nice to have a step by step analysis. Thanks :)
 
aldricj said:
Not sure how to even go about doing this problem. A rectangular banner has a red border and a white center. The banner has an 8 inch border at the top and the bottom, and it has a 6 inch border on each side. The total area of the banner is 27 ft squared or 3888 in squared. What should be the dimensions of the banner (x and y) if the area of the white center is to be a maximum? If possible, it would be nice to have a step by step analysis. Thanks :)
Click to expand...

Draw two rectangles - One inside the other (SYMMETRICALLY)

The length of the larger rectangle (banner) = L in

The Width of the larger rectangle (banner) = W in

The length of the smaller rectangle (center) = ??

The Width of the larger rectangle (banner) = ??

and continue.....

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
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