Multivariable Optimization problem
Postal regulations specify that the combined length and girth of a parcel sent by parcel post may not exceed 108 in. Find the dimensions of the rectangular package that would have the greatest possible volume under these regulations. (Hint: Let the dimensions of the box be x'' by y'' by z''. Then 2x + 2z + y = 108, and the volume V = xyz.
Show that V = f(x,z) = 108xz  2(x^2)z  2x(z^2). Maximize f(x,z).)
There will be three answers. The longest side, shortest side, and middle.
