A lively discussion is under way at Sunrise Software, where you are a project manager. The main question is whether the person-days concept has limitations. In other words, if a task will require 100 person-days, does it matter whether two people in 50 days, five people in 20 days, 10 people in 10 days, or some other combination that adds up to 100 performs the work

Yes.  It does matter.  There is another important consideration in project management.  This is the concept of project time or project delivery time.  Every project has an end date.  This implies that no project continues forever.  Just as there is a beginning, there is also an ending to every project.  This means that the project manager is concerned with whether the project will not exceed its allotted time frame.

Explanation:

Therefore, a project manager will not allow one person to execute a 100 person-days project just because it is feasible.  When she considers the project delivery time, she may decide to hire 10 persons to carry out the project, thus reducing the time to 10 days.  If a project is allowed to go on for a long time, it opens the opportunity for competitors to go to market first, thereby causing unprecedented losses to be suffered by the company.