Chapter 3, Problem 4E

Mark, Tim, Maia, and Kelly are dividing among themselves a set of common assets equally owned by the four of them. The assets are divided into four shares $\left(s_1,s_2\text{,}{s}_3\text{ and }{s}_4\right)$. $\underset{\_}{\text{Table }3-15}$ shows the values of the shares to each player expressed as a percent of the total value of the assets.

$Table3-15$

	$s_1$	$s_2$	$s_3$	$s_4$
Mark	20%	32%	28%	20%
Tim	25%	25%	25%	25%
Maia	15%	15%	30%	40%
Kelly	24%	26%	24%	26%

a. Which of the shares are fair shares to Mark?

b. Which of the shares are fair shares to Tim?

c. Which of the shares are fair shares to Maia?

d. Which of the shares are fair shares to Kelly?

e. Find all possible fair divisions of the assets using $s_1,s_2\text{,}{s}_3\text{, and }{s}_4$ as shares.