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Math Help - Student in a college prepare

  1. #1
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    Student in a college prepare

    Student in a college prepare a poster for display . The poster is to contain 200 sq inches of printed matter , with margins of 4 inches at top and bottom and of 2 inches on each side. Find the dimensions of the poster if the total area is to be minimum.
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  2. #2
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    Okay, this is an optimization problem.

    The first thing you are going to want to do is draw a picture - it really helps you visualize it. I set the length equal to y and the width equal to x. From the picture, you should be able to see that the length is equal to y-8 (eight being the size of the margins). You should also realize that the width is equal to x-4.

    Put this into the equation for area, A=x*y and you should get A=(y-8)(x-4)
    This doesn't help yet, but remember that A=x*y, and we want the printed area to be 200 sq inches. So, plug 200 in for A, and you get 200=x*y. Solve this for y, and you get y=200/x.

    Now plug that into your first area equation, and you get A=((200/x)-8)(x-4).

    From there, you should be able to simplify it and take the derivative. Once you have the derivative, it's simply a matter of optimizing the problem. Look for the critical points on the graph, and find the local maximum. Once you have a value for the local max, you should be able to return to the equation y=200/x. Just plug in the value of the relative maximum you found for x, and solve for y. From there, you should get your dimensions!

    Good luck!
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