Maximizing the Volume of a Box
If x was really small like 11000 of an inch you would only be folding the edges of the box up 11000 of an inch. What is the maximum volume of such a box. Grade 9 Optimization Review Sheet Ap Calculus Geometry Formulas Learning Math Maximizing the Volume of a Box A box with an open top is to be constructed from a square piece of cardboard 8 in. . Here the optimal dimensions of the box are and if we put two such boxes. So if we cut X inches from our rectangle. So x y 2 since x and y are non-negative. Starting with a rectangular sheet of metal we find the dimensions of the squares cut from each corner to give a box with maximum volume. 3x 2 12 0. Write the resulting function below. So the volume as a function of x is given by V x x 25 - 2 x 20 - 2 x. We get an equation which can be set equal to zero. By the way solutions to this sort of problem are typically nice in some sense. A square will ...