Asked by Alan
Mendoza Manufacturing plans to producea one compartment vertical file by bending the long side of a 10-in. by 18-in. sheet of plastic along two lines to form a U-shape. How tall should the file be in order to maximize the volume that it can hold?
Answers
Answered by
MathMate
The width is 10 in.
The long side is 18 in.
Let x be the distance of the bend from the edge, then the volume is
V(x) = 10x(18-2x)
Differentiate V(x) with respect to x to get V'(x).
Solve for x in V'(x) = 0 (solution = h)
Check that V"(h) (second derivative) is negative for a maximum.
If you have not done differential calculus before, please post again.
The long side is 18 in.
Let x be the distance of the bend from the edge, then the volume is
V(x) = 10x(18-2x)
Differentiate V(x) with respect to x to get V'(x).
Solve for x in V'(x) = 0 (solution = h)
Check that V"(h) (second derivative) is negative for a maximum.
If you have not done differential calculus before, please post again.
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