Kate and Faisal have utility functions that depend on their consumption of apples and oranges. There is a total supply of 16 apples and 14 oranges to divide between them. For the allocation to be considered "fair", Kate's utility must be at least 39 and Faisal's must be at least 36, and they must satisfy four additional inequalities comparing their individual consumptions and utilities.

1. Kate and Faisal have utility functions UK=4AK+OK and UF=AF+4OF respectively, where AK and
OK are K Kate's consumptions of apples and oranges and AF and OF are Faisal's consumptions
of apples and oranges. The total supply of apples and oranges to be divided between them is 16
apples and 14 oranges. The "fair" allocations consist of all allocations satisfying: 4AK+OK is at
least 39 and AF+4OF is at least 36. 4AK+OK is at least 78 and AF+4OF is at least 72. 8AK+2OK
is at least 78 and AF+4OF is at least 72. 8AK+2OK is at least 39 and 2AF+8OY is af least 72. 4AK
+OK is at least AK+4OF and AF+4OK is at least 4AK+OK.