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9 November, 00:07

If the garden is to be 2450 square feet, and the fence along the driveway costs $6 per foot while on the other three sides it costs only $2 per foot, find the dimensions that will minimize the cost.

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  1. 9 November, 00:27
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    Cost (C) = 8x + 4y

    For minimum cost C' = 0

    8 + 4dy/dx = 0

    dy/dx = - 2

    d (xy) / dx

    xdy/dx + y

    dy/dx = - y/x = - 2

    y = 2x

    x (2x) = 2450

    2x^2 = 2450

    x^2 = 1225

    x = √1225 = 35

    y = 2 (35) = 70

    Therefroe for minimum cost the dimension of the graden should be 35 by 70 feet.
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