An Economy Has Two People, Charlie and Doris

An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has an initial endowment of 3 apples and 10 bananas. Doris has an initial endowment of 6 apples and 5 bananas. Charlie's utility function is U(A C, B C ) = A C B C, where A C is his apple consumption and B C is his banana consumption. Doris's utility function is U(A D, B D ) = A D B D, where A D and B D are her apple and banana consumptions. At every Pareto optimal allocation,

A) Charlie consumes the same number of apples as Doris.
B) Charlie consumes 9 apples for every 15 bananas that he consumes.
C) Doris consumes equal numbers of apples and bananas.
D) Charlie consumes more bananas per apple than Doris does.
E) Doris consumes 6 apples for every 5 bananas that she consumes.