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

 Messages: [ Previous | Next ]
 Lynn Fisher (WOD) Posts: 64 Registered: 12/6/04
Re: Optimization Project
Posted: Dec 8, 1999 9:50 AM

In regards to Greg's answer, I don't think it's that simple because the problem
isn't simply to minimize area, it's to minimize cost. In fact, since the cost
of the lateral area is less, it's reasonable to assume a contrary
strategy...lower the area of the base and use a larger perimeter.

Here's where I got
A=area of base P=perimeter of base h=height of solid

The cost function c(A,P,h) = .01Ph+.05A

Since h = 355/A

C(A,P) = 3.55P/A + .05A

And I see no relationship between A and P to put this in terms of a single
variable.

I'm rusty on multivariable calculus, but I don't think there's a minimum for
the cost function except if A=0. Anybody better than me at multivariable that
wants to take it from there?

(In sum, I think the problem needs to have specified a regular base in order to
have a solution.)

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

Date Subject Author
12/6/99 Mygirls810@aol.com
12/7/99 Greg Spanier
12/8/99 Lynn Fisher (WOD)
12/8/99 Greg Spanier
12/9/99 Lynn Fisher (WOD)
12/9/99 Greg Spanier
12/8/99 Greg Spanier
12/9/99 Joshua Zucker
12/10/99 Lynn Fisher (WOD)
12/10/99 Lynn Fisher (WOD)
12/8/99 Dilks Stacey