The most critical aspect of the whole scenario is that you have to
present it to the customer service representative in the correct (ie,
their) orientation.  Otherwise you'll end up paying more since you've
turned the D into L, and H into D!

:-P

-Adam

On 6/11/07, Chris McSweeny <cpmcsweeny@gmail.com> wrote:
> Shame that's not the right answer :-)
>
> I did the same thing as Michael (but took a little longer). The answer is
> that L is twice D, H, which should presumably be intuitive...
>
> On 6/11/07, Denny Esterline <desterline@gmail.com> wrote:
> >
> > Well a sphere has the lergest volume/area ratio, but since you insist on
> > some sort of rectangular shape, a cube is the next best.
> >
> > And since cube means length=hieght=width...
> >
> > your equation becomes:
> > X+ 2(X+X) = 2000
> > or
> > 5X=2000
> > or
> > X=400
> >
> > So a 40cm cubed box is the largest volume you can ship and meet those
> > rules.
> >
> > (took longer to wite it than it did to do it in my head)
> >
> > -Denny
> >
> >
> >
> > On 6/11/07, Russell McMahon <apptech@paradise.net.nz> wrote:
> > >
> > > A diversion for those who can be bothered:
> > >
> > > Kristin is studying in Australia.
> > > The weather is getting cold lately.
> > > Russell & Valerie want to send her a box full of clothes, eiderdown,
> > > text books and more.
> > > The largest box that can be sent by parcel post is
> > >
> > >    Largest side <= 1000 mm
> > >    Sum of L +     2 x (D + H)  <= 2000 mm = Volume.weight = VW
> > >
> > >        L     length
> > >        D    depth
> > >        H    Height
> > >
> > > True volume is of course L x D x H
> > >
> > > Assignment for students:
> > >
> > >
> > >                What box dimensions maximise the true volume that can
> > > be sent?
> > >                Assume a rectangular box.
> > >
> > >                Report time to solve.
> > >
> > >
> > > The answer seems somehow obvious in retrospect but was annoyingly
> > > unintuitive (to me).
> > >
> > > Clue - of sorts:        John Crook will tell me that the answer is
> > > obvious on inspection using information theory (he'll be right).
> > >
> > >
> > >
> > >
> > >            Russell
> > >
> > >
> > >
> > >
> > > _____________________________
> > >
> > > Notes:
> > >
> > > 1.    I sent the parcel this evening - all 17.7 kg of it.
> > >
> > > 2.    Volume.Weight is actually a mongrel measure that is neither
> > > volume per weight.
> > >
> > > 3.    2 x (D+H) is the "girth" - the distance around the box.
> > > They seem to do it this way because they can do it with a pencil and
> > > paper (or in their head) more easily than using multiplication.
> > > What they REALLY want is volume.
> > > The ideal shape (from a sender's point of view) maximises the true
> > > volume per volume.weight.
> > >
> > > ie              maximises     L x D x H / ( L + 2x(D+H))
> > >
> > > However, for a fixed volume.weight, maximising volume does just as
> > > well so maximising
> > >
> > >    L x D x H while keeping
> > >
> > >        L + 2 x (D+H) = 2000 mm does the same thing.
> > >
> > > 4.    We had a nice black plastic box with lid, plastic clip in
> > > rollers and dimensions that *just* exceeded the allowable maximum VW
> > > if you took the very outer measurements in each case. As this was
> > > handles etc, and as the cross section was a trapezoid that was
> > > substantially smaller than D x H so true VW was well under the limit,
> > > it clearly met the spirit of the rules and MAY have met the letter
> > > depending on the mood of the clerk concerned. I used it. They didn't
> > > bother measuring it.
> > >
> > >
> > >
> > > --
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> > >
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> >
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