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have 50 sq ft of material to make an open top box with a square base.
a) use formula for surface area to express the height h of the box in terms of x.

b) find the dimensions of the box that will produce the maximum volume.

  • algebra -

    side of square = x
    height = h

    surface area = x^2 + 4xh

    x^2 + 4xh = 50
    h = (50 - x^2)/4x

    v = hx^2 = (50-x^2)/4x * x^2
    v = x(50-x^2)/4
    v has a max at x = 5sqrt(2/3) = 4.08

    so, a box 4 x 4 x 17/8 will have maximum volume of 34

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