He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an apertif

Question

"What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative B and alternative D. Furthermore, another transition point exists between alternatives C and D. What is this devilry, Hurwicz?"
Help Leonid Hurwicz identify the range of coefficients of optimism that render alternatives, B, C, and D superior to all others.

The cold, calculating father did exactly that when examining the 27 year old failure to launch man child that had turned his walk in closet into a bedroom. As he saw it, there were five alternatives; each had its advantages and disadvantages, and under different circumstances, each had a different financial incentive. He laid it all out neatly in a table, but as not to arouse suspicion, he left the table's labels very generic, so the alternatives were simply labeled A through E while the different circumstances were simply numbered one through three. He flicked the gray ash off of his favorite purple smoking jacket and pondered the best course of action under each possible future. It was good to be devious, he decided.

One Two Three
A 19 6 20
B 26 5 48
C 24 18 17
D 43 34 15
E 36 34 15

Answer 1

Answer: A coefficient of optimism from 0 up to 0.096 would make alternative C most attractive.
A coefficient of optimism from 0.096 up to 0.666 would make alternative D most attractive.
A coefficient of optimism beyond 0.666 would make alternative B most attractive.