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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 180000 square meters in order to provide enough grass for the herd. What dimensions would reuire the least amount of fencing if no fencing is needed along the river?
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  2. #2
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    Quote Originally Posted by got_jane View Post
    A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 180000 square meters in order to provide enough grass for the herd. What dimensions would reuire the least amount of fencing if no fencing is needed along the river?
    so you can make 2 equations form this
    180 000 = x*y for your area
    2x+y=P for your perimetre
    since there is 2 variables, use the equation with an answer to solve fora variable, lets solve for x
    x=180000/y
    plug this into your P equation
    2x+(180000/x)=P
    find the derivative
    2+(-180000/x^2)=P'
    Equate to 0
    -2x^2=-180000
    x^2=90000
    x=300
    Plug into original equation to solve for y
    180000=(300)*y
    y=600
    So your fence should be 300x600
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