My longest trip section without resupply is 14 days, but I didn't carry 14 days of food the whole way. I reckon good route planning is key.
I enjoyed a full traverse of the Western Arthurs, then walked to Melaleuca along the Port Davey track. Later, after resupply at Melaleuca, I walked the South West Cape Circuit.
I carried everything just 8klms, then stashed 4 days of food at Junction Creek for the Port Davey Track section, so I only carried 10 days of food up Moraine A.
I wasn't sure how I go, particularly those first few kays from the trailhead, but it all worked out fine!
I've currently got a trip spreadsheet going for a 19 day section without resupply in the Arthur Ranges, but every time I look at it I fell rather scared!

Check out this photo from 48 years ago when things were done a little differently .....
Retrieving Airdrops on Goon Moor, Eastern Arthurs, Federation Peak, SW Tasmania, 7th January, 1970. by
Dennis, on Flickr