I have been interviewed yesterday as a team leader for a start-up, and I was asked this:
Suppose you have a deadline for a client tomorrow and there is much pressure on your team to finish it and deliver the product on time. However, there is a client of yours that he needs an emergency support/fix otherwise he can not operate, run his business until it is fixed.
What would you do in this situation? Summarizing what I said, I would look all of my options, discuss with the team if there is a way to do both. If the answer is positive but we must work more hours today then I would choose this. If the answer was negative and I was sure that there is nothing we can do (even splitting the team is not helping), I would contact my new client telling him that the project will be delivered tomorrow and offer him an extended support or a discount/offer for our mistake. The team will work on our existing client.
He told me that there is no correct or false answer but there is a way to handle this better. I didn't ask why, and I need your opinions on what would be a better way to handle this.
For the record, I will have my reply soon.