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9 August, 17:44

A rectangular garden of area 300 square feet is to be surrounded on three sides by a brick wall costing $ 10 per foot and on one side by a fence costing $ 5 per foot. Find the dimensions of the garden such that the cost of the materials is minimized.

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  1. 9 August, 20:07
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    15 and 20 feet

    Explanation:

    The computation of the cost of the material minimized is shown below:

    As we know that

    Area of rectangle = Length * Width

    where,

    Length be X

    Width be Y

    So, the equation is

    X * Y = 300 square feet

    X = 300 : Y

    Now the another equation is

    C = 10 * (Y + Y + X) + 5X

    C = 20Y + 15X

    So we can write

    C = 20Y + 15 * 300 : Y

    C = 20Y + 4,500 : Y

    Now apply the derivatives

    So,

    DC : DY = 20 - 4,500 : Y^2 = 0

    20Y^2 = 4,500

    Y = 15

    So X = 20

    The C = Cost
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