The volume is LxWxH=36
we want the least surface area'
Since the top is opened, the total surface area = area of the bottom=LxW+sum of areas of the 4 sides=2xLxH+2x4xH=2LH+8H
plug in for L,2(36/4H)+8H=18/H+8H+4(36/4H)We want this to be minimum. find the first derivative, =0 ,find critical points Derivative WRT ,H
The area A=8H+54/H
dA/dH=8-54/H^2=0,solve for H and find the area and the amount