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RE: Optimization Project
Posted:
Dec 9, 1999 9:48 PM


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.
Greg
Original Message From: ownerapcalc@ets.org [mailto://ownerapcalc@ets.org] On Behalf Of Lynn A. Fisher Sent: Thursday, December 09, 1999 3:20 PM To: apcalc@ets.org 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: ownerapcalc@ets.org [mailto://ownerapcalc@ets.org] On Behalf Of > Mygirls810@aol.com > Sent: Monday, December 06, 1999 10:50 PM > To: apcalc@ets.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)6801601



