mathchads, i need you help:

in lego games you collects studs, which are basically money, at a fixed rate per level (let's say 100k studs per 1 level playthrough, but that's not the point)

additionally you can unlock studs multipliers, and each one costs studs to unlock (only once):
>2x: 1m studs
>4x: 2m studs
>6x: 3m studs
>8x: 4m studs
>10x: 5m studs

the thing is, you can stack multipliers, so if you unlock everything then you have a multiplier of 3840x for the normal studs rate (so in our example you'd get 384000k studs per level)

my question is: what's the fastest way to unlock ALL the multipliers? aka in which order should i buy them and how many levels would i need to play, assuming i earn 100k studs per level without multiplier.

if you can also explain why it would be appreciated

i think going in order would be the optimal strategy but i reached that conclusion after some light bruteforcing and i'm not entirely sure. also i would like to know if there is a formal way to prove that going in order is the best way (if that's the case)