finance/calc help???

Question

A shipping box is a rectanglular solid whose volume is 4ft^3. The length of the box is twice its width. The material to make The top and bottom costs $.30/ft^2 and the material for the sides costs $.20/ft^2. Find the dimensions of the box that will minimize the costs.

Answer 1

l=2w so V= 2w*w*h= 2w^2*h=4
C = 4w^2*30 +6w*h*20 (minimum)
C= 120w^2+120 w * 2/w^2 = 120( w^2+2/w)
C¨= 120 ( 2w-2/w^2 =0 so w^3-1=0 and w=1feet
l=2feet and h = 2feet