Are there any companies that deliver supplies (i.e., food, toiletries,
mail, etc.) to remote cabins in Alaska, and if so, WHAT ARE THEIR
TYPICAL PRICES and delivery schedules?

The cabin is:

(1) 50 air miles away from Anchorage, Alaska.
(2) Adjacent to a small lake that is suitable for the landing of float planes.

NOTE: The plane doesn't actually have to land: if they want to
delivery the supplies via airdrop or parachute, that's okay.

Fred Meyers purports to offer Alaskan Bush service...

http://www.fredmeyer.com/alaska/faqs.htm

Looks like the price is just 10% above whatever the normal price is.

God knows how they define 'bush'. It looks like you'd have to give them a call.