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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