What happens when you cannot reduce parts of the project that are on the critical path? How can that affect the outcome? (Remember throwing additional resources at things with a fixed duration won't change the duration?)

Going along with that train of thought - when the customer wants a project reduced - is it possible they would be willing to accept delivery of the unfinished project and finish it themselves? What do you think? How would you handle this situation?

Finally, there are instances when you cannot change the availability of your resources. Due to this you will be unable to reduce certain tasks on the critical path. What are some work around you could consider?