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Topic: Optimization Project
Replies: 10   Last Post: Dec 10, 1999 9:49 AM

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Greg Spanier

Posts: 66
Registered: 12/6/04
RE: Optimization Project
Posted: Dec 9, 1999 9:48 PM
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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: owner-ap-calc@ets.org [mailto://owner-ap-calc@ets.org] On Behalf Of Lynn
A. Fisher
Sent: Thursday, December 09, 1999 3:20 PM
To: ap-calc@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: owner-ap-calc@ets.org [mailto://owner-ap-calc@ets.org] On Behalf

Of
> Mygirls810@aol.com
> Sent: Monday, December 06, 1999 10:50 PM
> To: ap-calc@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)680-1601






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