anonymous
  • anonymous
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!
Mathematics
schrodinger
  • schrodinger
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misssunshinexxoxo
  • misssunshinexxoxo
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
  • anonymous
Thank you!
misty1212
  • misty1212
i am going to stick to my answer

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

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