   SEARCH HOME Math Central Quandaries & Queries  Question from Meghan, a student: Hi there, I have a question I've been working at for a while with maxima/minima of partial derivatives. "Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed. Find the dimensions of the rectangular package of greatest volume that can be mailed. (84 = length + girth = l + 2x + 2y)" I'm quite certain I'm supposed to substitute something, such as l = 84 - 2x - 2y. However, I've been having trouble setting the partial derivatives to zero and solving for a certain variable. Thank you so much for your help! -Meghan Hi Meghan,

You are to maximize the volume so you need an expression for the volume. The package is a "box" so the volume is given by V = l × x × y. You are correct in saying that l = 84 - 2x - 2y so substitute into the expression for the volume giving you the volume as a function of x and y.

Now try the partial derivatives. If you still have difficulties write back and tell us what you did.

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.