A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.) I got $236.15 Im not sure if its right, could someone check my answer please!

Question

misssunshinexxoxo · Answer

V=10m^3 
l=2w 
2w*w*h=V 
2w^2*h=10m^3 
h=10m^3/2w^2 

Aside=2*h*2w+2*h*w=2h(2w+w)=6hw 
Aside=6w*10m^3/2w^2 
Aside=30m^3/w 
Abottom=2w*w=2w^2 

COST=12*aside+20*Abottom 
Cost=12*30m^3/w+40w^2 
dcost/dw=-12*30m^3/w^2+80w 
*SET DERIVATIVE TO ZERO* 
12*30m^3/w^2=80w 
12*30m^3/80=w^3 
(12*30/80)^(1/3)=w 
1.65096362m=w 

Cost=12*30m^3/w+40w^2 
Cost=12*30/1.64096+40*1.65096^2 
Cost=$327.08

anonymous · Answer

Thank you!

misty1212 · Answer

i am going to stick to my answer

anonymous · Answer

I typed in the answer and got it right, so it is 327.08