Math

A farmer wants to fence in an area of 15000 m² in a rectangular field and then divide it into half with a fence parallel to one sides of the rectangle. How can he do this so as to minimize the cost of the fence?

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  1. Are you assuming 150 by 100? If so, the amount of fence would be 3(100)+2(150). Compare that to other possibilities, e.g., 300 by 50.

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  2. Let the long side by y m
    let the shorter side be x m
    So the area is xy and xy = 15000, -----> y = 15000/x

    For the cost to be minimum , the total amount of fencing has to be minimum
    F = 2y + 3x
    = 2(15000/x) + 3x
    dF/dx = -30000/x^2 + 3
    = 0 for a minimum of F
    3 = 30000/x^2
    x^2 = 10000
    x = 100 , then y = 15000/x = 150

    State your conclusion

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    Reiny

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