Find the rectangle of given perimeter that has greatest area by solving the firstorder necessary...

Find the rectangle of given perimeter that
has greatest area by solving the firstorder necessary conditions. Verify that
the second-order sufficiency conditions are satisfied.

The top, bottom, and front faces must be of
double weight (i.e., two pieces of cardboard). A posed is to find the
dimensions of such a box that maximize the volume for a given amount of
cardboard, equal to 72 sq. ft.

(a) What are the first-order necessary
conditions?