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Math Help - Maximizing a function.

  1. #1
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    Maximizing a function.

    Story problems always confuse me. Can someone point me in the right direction? Thanks!

    There are 544 yards of fencing available to enclose a rectangular field. How should this fencing be used so that the enclosed area is as large as possible? The area is maximized at length = ____ yards and width = ____ yards.
    Last edited by zsig013; April 8th 2008 at 03:44 PM.
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  2. #2
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    First create an equation for the area in terms of width and height.
    Find an equation of perimeter (2x width + 2x height).

    Isolate for one variable...it should be a parabola. Then if you are in calculus take the derivative and solve for 0. If not find the midpoint with -b/2a.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    OK here is what you do

    Quote Originally Posted by zsig013 View Post
    Story problems always confuse me. Can someone point me in the right direction? Thanks!

    There are 544 yards of fencing available to enclose a rectangular field. How should this fencing be used so that the enclosed area is as large as possible? The area is maximized at length = ____ yards and width = ____ yards.
    since it is a rectangle you know that 544=2x+2y,272=x+y and you know that Areas which is what you are trying to maximize is A=xy...using the substitution y\cdot(272-y)=272y-y^2=A we get our function we want to maximise diffrentiating we get A'=272-2y...which equals zero when y=136...before we yell hooray we need to check if it is a max or min so by diffentiating again we get A''=-2 so we know that y=136 is a max now subbing that back into your 272=x+y you can get your X value
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  4. #4
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    Okay, I took the derivative and get x=136. Making it a square (136*4=544). So It was simple as that Length and width both are 136? EDIT: Ahh Mathstud you're too quick. Thanks a lot!
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Haha

    Quote Originally Posted by zsig013 View Post
    Okay, I took the derivative and get x=136. Making it a square (136*4=544). So It was simple as that Length and width both are 136? EDIT: Ahh Mathstud you're too quick. Thanks a lot!
    Anytime thats what I come on for
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