2020 CIME II Problems/Problem 8
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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
.
Solution
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