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Question 456620: pleae help
one compartment vertical file is to be constructed by bending the long side of an 8 in by 12 in sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! one compartment vertical file is to be constructed by bending the long side of an 8 in by 12 in sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
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The sides of the drawer are formed by the long side of the sheet, so the depth of the drawer will be 8 in.
Since the depth of the drawer is fixed, it will play no role in the maximization problem.
So we need to maximize the area of the drawer formed by the two sides and bottom.
Let w = the width of the drawer
Let h = the height of the drawer
Then w + 2h = 12 [1]
The area, A = w*h [2]
Solve for w in [1] and substitute into [2]
w = 12 - 2h
A = (12-2h)h
To maximize the area compute dA/dh and set=0:
dA/dh = 0 = 12 - 4h
Solving for h gives h = 3
Therefore, the height is 3 in.
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