I just did a brief search through u tube and they have videos lasting any where from 42 days to over 100, with a KAYAK! Gawd knows how long it would take in a rubber life raft.
If he chose a good sea kayak he would have the ability to transport 400 pounds (weight includes operator). If Melvin was smart he would have purchased a good vacuum sealer and made up about 40x 1 day "Goody Packs" , each containing things like instant oatmeal, tea, hot chocolate, matches, salt/pepper packs, sugar packs, dehydrated soup and, small packages of kleenex, hard candys, etc. Then he could have chosen about 40 individual meals from Mountain House for example as his main meal of the day. A inflatable sleeping pad, sleeping bag and lightweight tarp, 100meters 550 cord, folding saw, medical kit, rifle 200 rds of ammo, pistol 100 rds, bug spray, sun screen, maps, compass, ground spikes for both anchoring the boat and holding down the tarp. And lets not forget a wet suit, life jacket and a set of plastic detachable wheels for the portaging of the kayak.