customise shipping rate with custom cart atrribute

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hi ive setup a custom cart attribute with

is a drop down selector with various suburbs/locations


we currently has a flat rate delivery charge, however i would like to trigger a different delviery rate based on the drop down selector. that is wehn customer choose drop down 1 it charges x amount delivery when the choose drop down 2 is charges y amount delivery. is this possible to acheive?