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I was curious and just priced everything out and you can get 20% more Mcdoubles/$ than sandwiches. 16 sandwiches with ham, lettuce, cheese, tomato, onion, mustard, mayo, salt, and pepper to 20 Mcdoubles. Calorie wise they are roughly even, I did not break it down by nutritional value but I would guess the sandwich would win on that. So you're right that you can get more Mcdoubles for your money but I'm right that you can get almost 16 sandwiches out of 40$ (and you will have leftover mustard, lettuce, salt, and pepper). If you get your condiments from stolen packets or catch sales on meat you can probably even out the cost of the two.
I appreciate that you did some earnest calculations. Normalizing for McDouble calorie counts is a decent way to do lateral comparisons. I did think about it, rather than napkin math, but then the CRM exploded at work, so I got distracted.