I've been out of the restaurant management business for about 5 years, but things couldn't have changed that much. It costs about 3 cents for the cup and about 10 cents on average to fill it (various size cups, not every refill is a full cup, etc). People get their initial fill, most people get one refill, few people get more than one. So, if we just assume everyone gets 2 refills, it costs 23 cents for your beverage, which they sell to you for anywhere from $1.50-$4 depending on the restaurant. That gets you a ~500% profit margin.
Fries also have a good margin, though there is a higher labor component, the cost of cooking them, keeping them frozen, lowered yield (waste, broken fries, etc). In fact, most fryer side orders are pretty profitable (a half dozen mozzarella sticks might sell for around $5, but you can buy a 4.5 pound case for around $11, which will yield about 10 orders).
The sandwiches aren't nearly as profitable, particularly the meat sandwiches, but the sandwiches are what get people in the door. A 1/3rd pound burger costs around 75 cents for the meat, 20 cents for the bun, 15 cents for the cheese, and up to another 25 cents if it is dressed. They need to be refrigerated, you lose yield (overcooked, fell apart, etc) and are relatively labor intensive (especially if you patty them yourself). For that $1.40 investment (not counting labor, yield, etc), you sell it for about $3.
Factor in that somewhere around a third of all of your revenue goes to labor and another 30-40% goes to food costs depending on your model. On top of that, you still have your overhead - mortgage/rent/property taxes, heating/cooling, gas/electric, etc. Profits are pretty thin in the fast food/diner/family restaurant market and without the profitability of the side orders, most of them can't stay in business for long (hell, most of these non-chain restaurants fail in the first year anyway). Upscale/fine dining is a whole different beast.
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