SOLUTION: A one compartment vertical file is to be constructed by bending the long side of an 8 in by 12 in. sheet of plastic along two lines to form a U shape. How tall should the file be t

Question 1058420: A one compartment vertical file is to be constructed by bending the long side of an 8 in by 12 in. sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The cross section would be a squared up U, with vertical sides inches tall,
and a middle horizontal section inches wide.
We really want to maximize the cross section area of the by rectangle,
because the 8 inch depth of the file is determined by the width of the 8 in by 12 in sheet of plastic.
The area of that cross section is
or
That is a polynomial of degree 2, or in other words a quadratic function.
We know that those are symmetrical functions with a minimum or maximum at their axis of symmetry (at the vertex of the parabola).
That maximum has to be exactly halfway between the zeros of the function,
which we knew would be at and (((x=6}}} before writing anything,
because those values correspond to no vertical sides, and no horizontal bottom respectively.
So, the file should be inches tall.

What did your teacher expect?
Maybe calculating volume as

and after that,
either calculating the derivative to find the value for the maximum,
or using the "formula"
to find the axis of symmetry of a quadratic function
.
RELATED QUESTIONS
pleae help one compartment vertical file is to be constructed by bending the long side (answered by htmentor)

A one compartment vertical file is to be constructed by bending the long side of an 8 in. (answered by ikleyn)

A one compartment vertical file is to be constructed by bending the long side of an 8... (answered by MathLover1)

Today's question, please help A one compartment vertical file is t be constructed by... (answered by Alan3354)

I have trouble with word problems,I don't know where to begin. The problem is Plastics... (answered by ankor@dixie-net.com)

I have this word problem that driving me nuts, the answer I got was forty inches and I... (answered by Alan3354)

You want to make a vertical file by bending the long side of an 8x14 inch sheet of metal... (answered by khwang)

A rectangular storage bin is to be made from a rectangular piece of sheet metal 16 in. by (answered by josgarithmetic)

An open box is to be constructed from a square sheet of plastic by removing a square of... (answered by psbhowmick)