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Math Help - optimization word problem

  1. #1
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    optimization word problem

    A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?
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  2. #2
    Senior Member nikhil's Avatar
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    Quote Originally Posted by cityismine View Post
    A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?
    HINT
    let length of rectangular field be a and width be b
    area =ab=c=1.5 million square feet(that is a constant)
    for minimizing the cost of fence perimeter(p) should be minimum.
    Let p=2(a+b)
    p=2(a+c/a)
    find dp/da and equate it to 0 to get the value of a
    then get value of b from ab=c
    Then divide the area by fencing parallel to the smaller side.
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