Chapter 3, Problem 5E

Allen, Brady, Cody, and Diane are sharing a cake. The cake had previously been divided into four slices $\left(s_1,s_2\text{,}{s}_3\text{, and }{s}_4\right)$. $\underset{\_}{\text{Table }3-16}$ shows the values of the slices in eyes of each player.

$Table3-16$

	$s_1$	$s_2$	$s_3$	$s_4$
Allen	$4.00	$5.00	$6.00	$5.00
Brady	$3.00	$3.50	$4.00	$5.50
Cody	$6.00	$4.50	$3.50	$4.00
Diane	$7.00	$4.00	$4.00	$5.00

a. Which of the slices are fair shares to Allen?

b. Which of the slices are fair shares to Brady?

c. Which of the slices are fair shares to Cody?

d. Which of the slices are fair shares to Diane?

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