SOLUTION: A manufacturer uses a 32 by 21 metal sheet to construct an open box by cutting out squares from each corner. What length square should be cut out to maximize the volume? Round answ

Question 487868: A manufacturer uses a 32 by 21 metal sheet to construct an open box by cutting out squares from each corner. What length square should be cut out to maximize the volume? Round answer to two decimal places.

I have tried this problems from many different angles, but I still cannot seem to get it right and I would love it if I could get some help. Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A manufacturer uses a 32 by 21 metal sheet to construct an open box by cutting out squares from each corner. What length square should be cut out to maximize the volume?
----
Draw a picture of the 32 by 21 sheet.
---
Draw the cut-outs that are x by x squares.
---
The dimentions of the box are now:
length: 32-2x
width: 21-2x
height: x
----------------
Volume = x(21-x)(32-x)
---
To find the maximum volume, take the
derivative of the cubic: dV/dx
--------
Set that equal to zero and solve to
find the value of "x" that gives you
the maximum volume.
===================================
Cheers,
Stan H.
RELATED QUESTIONS
a metal worker wants to make an open box from a sheet of metal, by cutting equal squares... (answered by Boreal)

A rectangular metal sheet whose length is 12cm longer than its width is crafted into an... (answered by ikleyn)

Sarah has two rectangular sheets of metal that measure 14 inches (in.) by 22 in. She... (answered by ankor@dixie-net.com)

A 20-inch square piece of metal is to be used to make an open-top box by cutting... (answered by ankor@dixie-net.com)

An open box is to be made from a rectangular sheet of tin by cutting out equal squares... (answered by josgarithmetic)

An open box is made from a square piece of sheet metal 19 inches on a side by cutting... (answered by stanbon)

A box with open top is formed from a square sheet of metal by cutting 30cm squares from... (answered by TimothyLamb)

An open box is to be constructed from a rectangular sheet of metal by removing a one-foot (answered by ankor@dixie-net.com)

An open Box is to be constructed from a square piece of sheet metal by removing a square... (answered by josgarithmetic)