What is the expected profit?
If I'm in state 1, the next trip will have average profit 8.8 (0.8 x 8 + 0.2 x 12). If I'm in state 2, the next trip will have average profit 11.2. The steady state values indicate that you are in state 1 about 60% of the time and in state 2 the other 40%, so I get 9.76 as the average profit.