Oh I didn't realize that the solution needed to include the actual formulas for transforming the data within TBM Studio...

My submission was only detailed in MS Excel where I laid out how I would configure the allocations.

Thank you to everyone who took the time to submit an answer!  As always, there is more than one way to implement a solution within Apptio. As most of you have determined, we were looking for a combination of what tower to use based on the information you had available, prioritizing the Activity Mapping over the Cost Center Mapping. Once doing so, we would be faced with a normalization question to make sure the hours still align so that it can be used as a weighting. 

There are multiple ways of implementing this but below are the formulas we used: 

For the Raw File  

Activity Map=Lookup({Activity },ActivityMap,{Activity },Tower and Subtower) 

Activity Subtower=Split(Activity Map,2,"-") 

Activity Tower=Split(Activity Map,1,"-") 

Allocation %=trim(split(CC Map,3,"-")) 

CC Map=LookupEx({CostCenter },CCMap,{Cost Center },Tower Subtower) 

CC Subtower=Split(CC Map,2,"-") 

CC Tower=Split(CC Map,1,"-") 

Final Hours={Allocation %}*{Actual Hours }/100 

Final Subtower=If(Activity Tower="",CC Tower,Activity Tower) 

Final Tower=If(Activity Subtower="",CC Subtower,Activity Subtower) 

For the Activity Mapping File 

Tower Subtower ={Tower }&&{Subtower } 

For the Cost Center Mapping File 

Tower Subtower ={Tower }&&{Subtower }&&{% }