how to get the largest AREA?

The fencing for the southern boundary costs $6 per foot, and the fencing for the east and west sides costs $3 per foot. If I have a budget of $240 for the project, what are the dimensions of the garden with the largest area I can enclose?

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  • 9 years ago
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    Area = xy, where x is the east-west length, and y is the southern boundary

    does this mean you're only fencing the east, west, and south sides, and the north side is against some border that doesn't need fencing?

    cost of fence: 6y + 2x(3) = 6x + 6y = 240

    x + y = 40

    y = 40 - x

    area = xy = x(40 - x)

    this is a parabola that opens downward with zeros at x = 0 and x = 40

    the vertex, a maximum, will be halfway between them at x = 20

    when x = 20, then y = 40 - 20 = 20

    the maximum area will be 20(20) = 400

    this will be with the east and west sides and southern side all having a length of 20

    the fact that the southern boundary is twice as expensive makes up for the fact that you aren't fencing the northern boundary

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