A box (with no lid) is to be constructed from a sheet of card board by cutting the squares from corners and folding up the sides. Suppose the original sheet of card board measures 16 inches by 16 inches. What would the size of the squares removed to maximize the volume of the resulting box?

Answer 1

v = x (16 - 2x)²

solve for the volume

take the 1st derivative (dv/dx), and set equal to zero

solve for x

test the two solutions