Three people will divide a 135-acre plot of land composed of 45 acres of rocky terrain, 30 acres of fields, and 60 acres of woods. Becky has no preference for one kind of land over another. John, who wants to start a small farm, has a preference ratio for field to woods to rocky terrain ratio of 5 to 3 to 2. Margaret loves the rocky terrain, and has a preference for field to woods to rocky terrain of 1 to 1 to 3.
a. If Margaret is the first divider and John is the first chooser, then find a proportional, envy-free division of the land.
b. Demonstrate that the division from part (a) is proportional by comparing the value each person places on their portion to the value they place on the entire 135 acres.
c. Demonstrate that the division from part (a) is envy-free by comparing the value each person places on his or her own portion to the value placed on the portions allocated to each of the other people.
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