You’re considering only variable costs, my friend. There are fixed costs too: store’s rent (or the opportunity cost if you own), insurance, etc. Anyways, thanks for the entertainment and going into the minutiae of burger selling. I could have said “$300 airfare” or “$0.75 pen”, etc.
I’m considering those costs that depend on exchange rates. When dollar goes down, it directly affects prices of things we import and prices of things we can export. Burgers are neither.
Aha! You assume that the money supply is constant. Now your burger example starts to make more sense. But that’s an enormous IF you use. The metaphorical printing presses are working at full steam!