Chapter 3, Problem 6E

Carlos, Sonya, Tanner, and Wen are sharing a cake. The cake had previously been divided into four slices $\left(s_1,s_2\text{,}{s}_3\text{, and }{s}_4\right)$. $Table3-17$ shows the values of the slices in eyes of each player.

$Table3-17$

	S1	S2	S3	S4
Carlos	$3.00	$5.00	$5.00	$3.00
Sonya	$4.50	$3.50	$4.50	$5.50
Tanner	$4.25	$4.50	$3.50	$3.75
Wen	$5.50	$4.00	$4.50	$6.00

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

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

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

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

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