This is the 11352nd most frequent Swedish word.
möjligast
"Möjligast" means "as possible" or "to the greatest extent possible."
This sentence uses 'möjligast' (most possible) as an adverb to express the utmost degree of efficiency attainable.
Vi ska försöka lösa problemet på möjligast effektivt sätt.
We will try to solve the problem in the most efficient way possible.
Here, 'möjligast' is used to emphasize the urgency and maximum speed achievable in the context.
Kom tillbaka så möjligast snabbt du kan.
Come back as quickly as you possibly can.
In this case, 'möjligast' modifies the adjective 'billigaste' to indicate the extreme least costfulness within feasibility.