A new cell-phone company advertises a phone plan. For $30.60, the user can have 1100 weekday minutes, 1100 weeknight minutes, and 1100 weekend minutes. Duane, Doreen, and Kaylee will divide the minutes using the divide-and-choose method for three players.
a. If Duane has no preference, and he values weekday, weeknight, and weekend minutes equally, what monetary value would he place on each set of minutes? What value would he require in order to consider a share of minutes to be a fair share?
b. If Doreen prefers weekday and weeknight minutes over weekend minutes in a ratio of 2 to 2 to 1, what monetary value would she place on each set of minutes? What value would she require in order to consider a share of minutes to be a fair share?
c. If Kaylee’s weekday to weeknight to weekend ratio is 1-to-2-to-3, what monetary value would she place on each set of minutes? What value would she require in order to consider a share of minutes to be a fair share?
d. Duane is the divider, and he creates the following three plans:
Plan I: 400 weekday minutes, 150 weeknight minutes, 550 weekend minutes
Plan II: 300 weekday minutes, 350 weeknight minutes, 450 weekend minutes
Plan III: 400 weekday minutes, 600 weeknight minutes, 100 weekend minutes
Determine the result of the divide-and-choose method for three players.
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