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...

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 $teve’s optimal strategy for dealing with his roof.