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If 1500 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Volume =

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Tim

  1. let the base be x cm by x cm, and the height y cm

    then x^2 + 4xy = 1500
    y = (1500 - x^2)/(4x)

    V = x^2y
    = x^2(1500 - x^2)/(4x)

    expand, find dV/dx
    set that equal to zero and solve

    let me know how you made out.

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    Reiny

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