Jeff Kaufmann’s machine shop sells a variety of machines for job shops. A customer wants to purchase a model XPO2 drilling machine from Jeff’s store. The model XPO2 sells for $180,000, but Jeff is out of XPO2s. The customer says he will wait for Jeff to get a model XPO2 in stock. Jeff knows that there is a wholesale market for XPO2s from which he can purchase an XPO2. Jeff can buy an XPO2 today for $150,000, or he can wait a day and buy an XPO2 (if one is available) tomorrow for $125,000. If at least one XPO2 is still available tomorrow Jeff can wait until the day after tomorrow and buy and XPO2 (if one is still available) for $110,000.
There is a 0.40 probability that there will be no model XPO2s available tomorrow. If there are model XPO2s available tomorrow, there is a 0.70 probability that by the day after tomorrow, there will be no model XPO2s available in the wholesale market. Three days from now, it is certain that no model XPO2s will be available on the wholesale market. What is the maximum expected profit that Jeff can achieve? What should Jeff do?