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?

Answer 1

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.