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14 October, 03:52

The fencing of the left border costs $4 per foot, while the fencing of the lower border costs $1 per foot. (no fencing is required along the river.) you want to spend $64 and enclose as much area as possible. what are the dimensions of your garden, and what area does it enclose? hint [the area of a right-triangle is given by

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  1. 14 October, 07:32
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    Answer

    Left border = 8 feet

    Lower border = 32 feet

    Area=128 〖ft〗^2

    Explanation

    The area is a right triangle.

    Let us take the left border to be y feet and the lower border to be x feet

    Area=1/2 yx

    The cost of fencing would be 4y+x=64.

    From this expression x=64-4y

    Substituting this value of x in the area we have;

    Area=1/2 y (64-4y)

    A=32y-2y^2

    To get the maximum area of the triangle the first derivative of the area would te equal to zero.

    A=32y-2y^2

    dA/dy=32-4y=0

    4y=32

    y=8

    Since x=64-4y

    x=64 - (4*8) = 32

    The dimensions of the garden are 8 feet by 32 feet.

    Since the garden is a right triangle,

    Area=1/2*8*32

    Area=128 〖ft〗^2
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