A 5 cm by 5 cm square is cut from each corner of a rectangular piece of cardboard. The sides are folded up to make an open box with a maximum volume. If the perimeter of the base is 50 cm, what are the dimensions of the box?

Answer 1

If the cardboard had dimensions x and y, then
2(x-10 + y-10) = 50
x+y = 45
Now, the volume is
v = 5(x-10)(y-10) = 5(x-10)(35-x) = -5(x^2-45x+350)
The vertex of this parabola (maximum volume) is at (45/2 , 3125/4)