Chapter 3, Problem 2E

Alice, Bob, and Carlos are dividing among themselves the family farm equally owned by the three of them. The property is divided into three shares $\left(s_1,s_2\text{ and }{s}_3\right)$. Table 3-13 shows the values of the shares to each player expressed as a percent of the total value of the property.

Table 3-13

	S1	S2	S3
Alice	38%	28%	34%
Bob	3313%	3313%	3313%
Carlos	34%	40%	26%

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

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

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

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

e. Of the fair divisions found in (d), which one is the best?