What is the difference between a constrained and an unconstrained analysis?

An unconstrained analysis assumes that there is no limit on, say, the amount of money that can be spent on advertising or the number of sales reps that can be hired.

It provides both the optimal total level of spending and the allocation of that spending to segments. A constrained analysis provides the allocation of spending only, given the constraints imposed on overall spending, on spending in different segments, or both.