Two years ahead a company called Mango will need to decide between one of three decisions: continue to market its current machine M0 (d0), market a new version Mi of its old product (d1) or market a replacement machine M2 (d2). The machines M1 and M2 can only be marketed if they have been successfully developed: events which are judged by Mango to have respective probabilities 0.9 and 0.6. The cost of developing M1 is $3m and M2 is $5m and the company can choose to develop either or both of M1 and M2. The expected net profits from M0, M1 or M2 if successfully developed are $2m, $10m and $18m. Use a rollback tree to calculate the decision rule maximizing the company expected payoff