When we lived in Bethel, a bush community 400 air miles off the US road system, it was common to spend $9 on milk, $20 on OJ, $5 on bread, $60 on watermelon. Yes, $60 for watermelon. Routinely, I would spend $6 per pear. It was bad and yes, in the bush, most everything is air lifted in. During the summer, things can be barged in - but that's only for about 4 months.
Now I live in southcentral Alaska, and prices are reasonable. But like AKP said, Anchorage is a much cheaper part of the state.
Besides, you learn the tricks. Both Walmart and Fred Meyers will ship orders to you, including groceries. You can either call and place your order, order online or go to the store and they'll ship it all to you. Span Alaska is another good way to order groceries and supplies in bulk from Washington and it will be sent to you via barge in the summer time. Real good way to get paper goods, cereals, canned goods, etc. Drugstore.com is also really good for getting your personal items - and much cheaper if you're not on the road system.
It is very expensive here, but you do learn how to stretch a dollar.