So in accounting there are 3 responsibility centers which are:

Cost Center
Profit Center
Investment Center

Why do these 3 need separate budgets?

3 answers

I would add a fourth responsibility center, the revenue center. Why do the need separate budgets? So they can be monitored, and controlled, and someone can be accountable for revenue, cost, profit, and investments.

http://maaw.info/ResponsibilityAccountingConcept.htm
Thanks.

So, if you were to give an example of the kinds of decisions where incremental analysis would be used in each center, what examples would you give?
http://www.plu.edu/~mgtacctg/incremental_analysi.htm

We will be happy to critique your thinking.