Th long side of the plastic sheet is bent into a U shape.
Therefore the dimensions of the file holder are 8, h, and (10 - 2h) as shown in the figure.
The volume of the file holder is
V = 8*h*(10 - 2h) = 80h - 16h²
To maximize V, V'(h) = 0.
That is,
80 - 32 h = 0
h = 80/32 = 2.5 in
V''(h) = -32 guarantees that V is maximum because V'' <0.
Maximum V = 80*(2.5) - 16*(2.5)² = 100 in³
Answer: h = 2.5 in
Therefore the dimensions of the file holder are 8, h, and (10 - 2h) as shown in the figure.
The volume of the file holder is
V = 8*h*(10 - 2h) = 80h - 16h²
To maximize V, V'(h) = 0.
That is,
80 - 32 h = 0
h = 80/32 = 2.5 in
V''(h) = -32 guarantees that V is maximum because V'' <0.
Maximum V = 80*(2.5) - 16*(2.5)² = 100 in³
Answer: h = 2.5 in