Thread: Optimization Problem

I just need a little help getting started. Any help is appreciated!


A company has 900 employees who are divided into x teams of equal size, which compete against each other for bonuses. Each year, the winning team gets a bonus for each team member. However, one bonus is also given out to one member of each of the other teams. Into how many groups must the employees be divided so that the number of bonuses is minimized?

x= number of teams
p= number of people per team

x=(900)/p

b= number of bonuses

b= x+p
b= (900)/p + p

derive and set db/dx equal to zero