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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