Three business partners want to divide the mining rights on a mountain. There are 30 square miles on the east side, 60 square miles on the west side, and 12 square miles on the south side of the mountain. Harmon’s east to west to south preference ratio is 2 to 1 to 1, Darnell’s preference ratio is 1 to 3 to 1, and Parker’s preference ratio is 3 to 2 to 1. They will use the last-diminisher method to divide the land.
a. Using points to represent the value a partner places on each square mile, how would each partner assign values to the three pieces of land and how many points would represent a fair share to each of the partners?
b. Suppose Harmon is the lone divider, and he creates the following package: 14 square miles on the east side, 12 square miles on the west side, and 4 square miles on the south side. Verify that this package represents a fair share according to Harmon’s values.
c. The package from part (b) will pass to Darnell and then to Parker. Explain whether or not either of these partners will trim the package, how the package will be trimmed, and who gets the package or the trimmed package.
d. Determine how the remaining two partners can split the remaining land fairly using the divide and- choose method for two players.
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