Originally Posted by

**heebee** This is my first post and involves optimization of the most economic shape of a can. The problem verbatim is "Let's assume that most of the expense is incurred in joining the sides to the rims of the cans. If we cut the discs from hexagons as in task #4, then the total cost is proportional to

$\displaystyle 4*3^{1/3}r^2+2\pi rh+k(4\pi r+h)$

where k is the reciprocal of the length that can be joined for the cost of one unit area of metal. Show that this expression is minimized when:

$\displaystyle V^{1/3}/k= ((\pi h)/r)^{1/3} * (2\pi-h/r)/(\pi h/r-4*3^{1/3})$

I have no idea where to begin with this one. Any help is much appreciated.