If you don't minimize the perimeter for any given area and height, you simply incur needless cost by keeping the same volume, but with greater lateral area than necessary.
-----Original Message----- From: email@example.com [mailto://firstname.lastname@example.org] On Behalf Of Lynn A. Fisher Sent: Thursday, December 09, 1999 3:20 PM To: email@example.com Subject: Re: Optimization Project
Greg Spanier wrote:
>x = cuberoot(14.2 / 0.45) = 3.16 approx, for which the cost is 3.89 cents >approx.
>I hope this is right <smile>
I got that, too, but I still don't agree with your argument about the perimeter needing to be minimized, and I haven't gotten an opportunity to review your multivariable argument. I'm working on finding a counterexample!
Lynn Fisher Woodstock Union HS Woodstock, VT
Greg Spanier wrote:
> The surface area of the lateral faces depends upon the perimeter of the base > (and, of course, the height.) To minimize the perimeter of a polygon of any > given area, and hence the lateral area, the polygon needs to be regular. > However, I do think the question probably should have specified that the > hexagon be regular. > > Hope this helps, > > Greg > > -----Original Message----- > From: firstname.lastname@example.org [mailto://email@example.com] On Behalf Of > Mygirls810@aol.com > Sent: Monday, December 06, 1999 10:50 PM > To: firstname.lastname@example.org > Subject: Optimization Project > > Hi All, > > I recently assigned a project to my AB class and we are encountering some > confusion. If anyone could clarify things it would be appreciated. I got > the project from "A Watched Cup Never Cools" put out by Key Curriculum
> Press. > The name of the project is PRISM POP. The set up is as follows: > > Your team has been given the assignment of submitting a packaging plan > for a new product. Prism Pop is a soda to be sold in hexagonally based > cans, > each holding 355 milliliters of pop.The management prefers plans that lower > the cost. The material for the sides costs 0.01 cents per square > centimeter. > The material for the bottom costs 0.03 cents per square centimeter. The > material for the top costs 0.02 cents per square centimeter. > > My question is this: the problem did not specify that the base had to be a > REGULAR hexagon even though the diagram accompanying it did show a regular > hexagon. If the base is not regular, how could you find the cost of the > area > to minimize? I may be missing something obvious, but I really am stumped on > this one. All help is greatly appreciated. > > Thanks, > Jeanne M. Benecke > Mygirls810@aol.com > Tappan Zee High School > Orangeburg, NY 10965 > (914)680-1601