2020 CIME II Problems/Problem 8
A committee has an oligarchy, consisting of of the members of the committee. Suppose that of the work is done by the oligarchy. If the average amount of work done by a member of the oligarchy is times the amount of work done by a nonmember of the oligarchy, find the maximum possible value of .
Average work done sets up an equation: Let and : Complete the squares:
Note that so must use minus. This means that C is maximized if is at a maximum