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March 24, 2017

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A farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). The pasture must contain 320,000 square meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river?
x = m
y = m


Plz help...thnks

  • calulus - minimum - ,

    Since length x width = area
    we have length=area/width

    Let
    w=width of the pasture, and
    320000/w=length (parallel to river) of pasture
    Total length of fencing
    F=twice width + length
    =2w + 320000/w

    Find derivative of F with respect to w and equate to zero to find w.
    i.e.
    Solve for w in
    dF/dw=0

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