Produce a one compartment vertical file by bending the long side of an 10-in. by 18-in. sheet of plastic along two lines to form a U-shape. (i)How tall should the file be in order to maximize the volume that the file can hold? (ii) What is the maximum volume?
Bend on lines so that the file is 10 long x Y high x (18 - 2Y) thick Volume = V = 180Y - 20Y^2 dV/dY = 180 - 40Y = 0 when V is maximum. Y = 9/2 For max. volume file is = 10 x 9/2 x 9 Max V = 405 cubic ins.
