Response to the following problem:
Steve Johnson believes that this winter is going to be extremely rainy, and he is trying to decide whether he should repair or replace his roof. Steve can install a new roof for $7000 or have it repaired for $1000. While the repair work will probably mean that the house will not have any leaks during the upcoming year, Steve believes that he will definitely need a new roof next year and would have to pay $7000 at that time if he does not get the roof replaced this year. There is a 60% chance that Steve will be transferred during the upcoming year and will have to put his house on the market. Steve feels that a new roof will enable him to get $4000 more if he sells his house. If he does not repair or replace the roof Steve believes there is a 70% chance that there will be rain damage to his home. He estimates the likelihood that the damage will be $500 is .10, $1000 is .20, $1500 is .30 and $2000 is .40.
Using a decision tree analysis, determine steve's optimal strategy for dealing with his roof.