# 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

\[C = \frac{1700}{15} - \frac{8 \times 100}{15}} = 900/15=60\] (Error compiling LaTeX. ! Extra }, or forgotten $.)

is at a maximum