# Difference between revisions of "2020 CIME II Problems/Problem 8"

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<cmath> C = \frac{1700}{15} \pm \sqrt{(D-100)^2 + \frac{8^2 \times 100^2}{15^2}}</cmath> | <cmath> C = \frac{1700}{15} \pm \sqrt{(D-100)^2 + \frac{8^2 \times 100^2}{15^2}}</cmath> | ||

− | Note that <math>\frac{1700+800}{15}> | + | Note that <math>\frac{1700+800}{15}>100</math> so must use minus. This means that C is maximized if <math>D=100</math> |

<cmath> C = \frac{1700}{15} - \frac{8 \times 100}{15} = 900/15=60</cmath> | <cmath> C = \frac{1700}{15} - \frac{8 \times 100}{15} = 900/15=60</cmath> | ||

<math>B-A</math> is at a maximum <math>60</math> | <math>B-A</math> is at a maximum <math>60</math> |

## Latest revision as of 13:59, 19 January 2021

## 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