Problema Solution
A one compartment vertical file is t be constructed by bending the long side of an 8in by 14 in plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold.
Answer provided by our tutors
9The 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 = 14 (1)
The Volume, v = w*h *8
It will be maximum if w*h is maximum
let A=w*h (2)
Solve for w in [1] and substitute into [2]
w = 14 - 2h
A = (14-2h)h
To maximize the area compute dA/dh and set=0:
dA/dh = 0 = 14 - 4h
Solving for h gives h = 14/4=7/2=3.5
Therefore, the height is 3.5 in.