A firm wants to manufacture an open steel container with a capacity 4l. Determine the dimensions of the container with a square base if they want to use the minimum amount of sheet metal
if the base is x and the height is z, then
x^2z = 4
The surface is the base and 4 sides, so
a = x^2 + 4xz
= x^2 + 4x(4/x^2)
= x^2 + 16/x
da/dx = 2x - 16/x^2
= (2x^3-16)/x^2
da/dx = 0 when x=2, so the container is 2x2x1