Suppose That Paul and David Have Utility Functions U =

Suppose that Paul and David have utility functions U = 4A P + O P and U = A D + 5O D, respectively, where A P and O P are Paul's consumptions of apples and oranges and A D and O D are David's consumptions of apples and orange. The total supply of apples and oranges to be divided between them is 20 apples and 14 oranges. The "fair" allocations consist of all allocations satisfying the following conditions.

A) 4A_P + O_P is at least 94 and 2A_D + 5O_D is at least 90.
B) A_D + O_D is at least 17 and A_S + O_S is at least 17.
C) A_D = A_P and O_D = O_P.
D) 8A_P + 2O_P is at least 94 and 2A_D + 10O_D is at least 90.
E) 4A_P + O_P is at least A_D + 5O_D and A_D + 5O_D is at least 4A_P + O_P.

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