Question

Suppose 15 peaches and 20 oranges need to be divided between fred and ethel. Fred's utility function is U=Max(#of peaches, #of oranges) ethels utility function is U=Max(2# peaches, # of oranges). Carefully draw a graph showing the set of Pareto efficient allocations.

Answer 1

I don't understand your Utility functions. If I read your post, literally, then:
If Fred has 1 peaches and 10 oranges, his utility is same as if he had 9 peaches and 10 oranges. The utility for both mixes is 10? This does not make sense.