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Thread: optimization problem

  1. #1
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    optimization problem

    A farmer wishes to fence an area next to his barn. He needs a wire fence that costs $1 per linear foot in front of the barn and and wooden fencing that costs $2 per foot on the other sides.
    Find x and y so that he can enclose the maximum area if his budget for materials is $4400.


    $\displaystyle A=2xy$

    $\displaystyle c=(2*2x) + (1*y)=4400$

    $\displaystyle 4x=4400-y$

    $\displaystyle x=1100-\frac{y}{4}$

    $\displaystyle A=2(1100-\frac{y}{4})y=2200y-\frac{y^2}{2}$

    $\displaystyle A'=2200-y$

    $\displaystyle y=2200
    $

    Y is supposed to be $\displaystyle \frac{2200}{3}$.
    So either my area function or my constraint is wrong?
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  2. #2
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    Does the problem say rectangular area? If so,

    You're area should just be xy, if you draw a picture you will see this, you need the 2 in there when considering cost, as you have done
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  3. #3
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    why do you think Y is incorrect? because I am actually getting 2200 and 550
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  4. #4
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    They had a picture like this:

    where W was labled "$\displaystyle x$", and L was labeled "$\displaystyle y$". The top horizontal piece opposite the "L" was labeled "$\displaystyle barn(wire)$."

    I still ended up getting $\displaystyle y=2200$, when I did $\displaystyle A=xy $though.

    $\displaystyle A=(1100-\frac{y}{4})y$
    $\displaystyle 1100y-\frac{y^2}{4})$
    $\displaystyle A'=1100-\frac{y}{2})$
    $\displaystyle 1100=\frac{y}{2}$
    $\displaystyle y=2200$
    ?
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  5. #5
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    Quote Originally Posted by artvandalay11 View Post
    why do you think Y is incorrect? because I am actually getting 2200 and 550
    Here are the solutions: http://www.math.ufl.edu/~jysmith/MAC...0answerf09.pdf

    This is #22.
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  6. #6
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    Yes I'm sorry about the xy comment, I realized it wouldnt make a difference for your Y value since the 2 goes away when you differentiate, but that answer has to be incorrect


    We both agree on Cost:

    $\displaystyle C=2(2x)+1(y)=4x+y=4400$

    Now let's try the "answer"

    $\displaystyle 4(550)+\frac{2200}{3}=2200+\frac{2200}{3}\not =4400$
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  7. #7
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    Y would equal $\displaystyle \frac{2200}{3}$ if the cost for that side of fencing was $3 per foot
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  8. #8
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    That is true. I guess I'll have to straighten that out with my professor.Well, anyways .
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