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A box with an open top is to be constructed from a square piece of cardboard, 9 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume such a box can have.
An open box is to be made from a piece of cardboard by cutting squares out of each corner and folding up the sides. If the size of the cardboard is 2 ft by 3 ft, what size squares (in inches) should be cut out to maximize the volume of the box?