# Maximum possible volume?

• Nov 18th 2009, 01:31 PM
mathcalculushelp
Maximum possible volume?
The US postal office stipulates that any boxes sent through the mail must have a length plus girth(distance around) totalling no more than 108 inches.Find the dimensions of the box with the maximum possible volume that can be sent through the US mail assuming that width and height are equal.Set up an appropriate model and use corresponding derivative function to justify your answer.
• Nov 18th 2009, 01:38 PM
skeeter
Quote:

Originally Posted by mathcalculushelp
The US postal office stipulates that any boxes sent through the mail must have a length plus girth(distance around) totalling no more than 108 inches.Find the dimensions of the box with the maximum possible volume that can be sent through the US mail assuming that width and height are equal.Set up an appropriate model and use corresponding derivative function to justify your answer.

\$\displaystyle L+4W = 108\$

\$\displaystyle V = LW^2\$

get volume, \$\displaystyle V\$ , in terms of a single variable and maximize.