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You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the following dimensions will give you the greatest volume?

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  1. 12 May, 04:32
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    Suppose you cut squares have the side lengths x then we have

    length of base box=20-2x

    width of base box=30-2x

    height of box=x

    volume of the box

    V=x (20-2x) (30-2x)

    V=600x-100x^2+4x^3

    then

    dV/dx=600-200x+12x^2

    set that to zero

    600-200x+12x^2=0

    apply quadratic formula

    x=approx12.97 or 3.92

    since you want in whole numbers so x=13 or x=4

    so if x=13 then V = - 312 but negative number doesn't make a sense so we ignore that

    if x=4 then v=1056 this is the greatest volume

    the dimensions are

    length of a box base=12

    width of a box base=22

    height of box = 4

    did u get it?
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