Sending a parcel

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Problem

Sending a Parcel printable sheet



The Post Office used to have a strange way of limiting the size of parcels. The maximum allowed was "6 feet combined length and girth". That meant you added together the distance round the middle of the parcel (that's the girth) and the length.

Image
A diagram showing what the girth of a parcel would be; the distance around the middle of the parcel.



You could have sent a fishing rod very nearly 6 feet long and just a few inches round the girth!

Bringing the problem up-to-date, let's set the maximum combined length and girth to be 2 metres (which is a bit more than 6 feet).

What is the greatest volume you can now get for a cuboid parcel with whole centimetre dimensions?