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

Dark adonis (talk | contribs) (Created page with "==Problem 8== A committee has an oligarchy, consisting of <math>A\%</math> of the members of the committee. Suppose that <math>B\%</math> of the work is done by the oligarchy....") |
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Note that <math>\frac{1700+800}{15}>1</math> so must use minus. This means that C is maximized if <math>D=100</math> | Note that <math>\frac{1700+800}{15}>1</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 | + | <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> |

## Revision as of 14:58, 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