SOLUTION: A company wishes to manufacture a box with a volume of 36 square feet, has an open top and is twice as long as it is wide. Find the dimensions of the box produced from the minima

Question 202176: A company wishes to manufacture a box with a volume of 36 square feet, has an open top and is twice as long as it is wide. Find the dimensions of the box produced from the minimal amount of material.

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
36 cubic feet
.
Dimensions are L=2w,,W=w, H=h
.
volume = L*W*H= 2w*w*h=2w^2h =36,,,w^2h =18
.
Surface area = 2w*w + 6w *h,,,,Area of base + perimeter *h
.
h,,,,,,,,,,w (sqrt 18/h),,,,,,SA (2w^2 +6wh)
.
1,,,,,,,,,,4.24,,,,,,,,,,,,,,,,61.41
.
1.875,,,,,,3.098,,,,,,,,,,,,,,54.05
.
2,,,,,,,,,,3,,,,,,,,,,,,,,,,,,54,,,,,,,,,,,,,,,Min SA,,,L=6,w=3,h=2
.
2.125,,,,,,2.910,,,,,,,,,,,,,,54.044
.
3,,,,,,,,,,2.449,,,,,,,,,,,,,,56.086
.
checking, vol = 3*6*2 = 36 ok
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