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

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Joshua Zucker

Posts: 212
Registered: 12/4/04
Re: Optimization Project
Posted: Dec 9, 1999 11:48 AM
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>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.


For any given fixed value of A, C(A,P) is minimized when P is as
small as possible. That's why the regular hexagon is best for
any value of A you pick.


--Joshua Zucker
Gunn HS, Palo Alto, CA
http://www.gunn.palo-alto.ca.us/teacher/jzucker/





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