No, not at all -- it's the costs of printing the bookblock that are the same for both the regular and "variant" editions, because those bookblocks are all printed at the same time, as part of the same press run. (I use the term in quotes because in every substantive way, the books are identical.)

There doesn't need to be any correlation between the quantities -- it's just that some of the books are packaged with one cover, a few are packaged with a different cover. The books with a "different cover" can be as few or as many of the print run as are needed.

(DC used to do something like this with hardcovers and trade paperbacks -- all of the bookblocks for both versions would be printed at the same time, the hardcovers would be bound and the materials for the trade paperbacks would go into storage, to be bound at a later date. You get a better price-per-unit because the quantities are better.)

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