Question 1071558
The box can be made from a 3 m x 4 m sheet of metal by cutting squares from the corners and folding up the sides.
:
One way is t0 plot the equation y = x(4-2x)(3-2x), y being the volume
{{{ graph( 300, 200, -1, 2, -4, 6, x*(4-2x)*(3-2x)) }}}

1. What is the maximum volume of the box?
Max occurs when x=.566 inches, then y = 3.032 cu/m
:
2. What are the box's dimensions?
Height = .566 m
4 - 2(.566) = 2.87 m is the length
3 - 2(.566) = 1.87 m is the width