An engineer wants to buy a packaging machine to replace an inoperable one. She has two option: to buy a brand-new machine for $60,000, or two buy a used (second-hand) one for $40,000 but with no warranty. In both cases, the present value (PV) of future revenues generated by the machine is $100,000, assuming that the used machine is in a good condition. However, there is a possibility that the used machine is in a poor condition (faulty), in which case it has to be scrapped at a salvage value of $20,000 only. To reduce uncertainty about the used machine condition, the engineer has decided to inspect it. There are two types of tests available: A Quick Test (QT) which costs $3000 and a Comprehensive Test (CT) which costs $6000.

 QT has a 70% accuracy in detecting faulty machines and 80% accuracy in detecting machines in a good condition. CT has a 90% accuracy in detecting the right condition of the machine, whether it is faulty or in a good condition. By test accuracy we mean that, given a certain condition of the machine, the test result is consistent with it. For example, the probability of a positive test result (PTR) when the machine is in a good condition is 90% for CT. 

Past experience with the used machines supplier has shown that 40% of its machines were faulty. Use a decision tree to select the test to be conducted (QT or CT) and the machine type (brand-new or second-hand) to be purchased based on the test result and to compute the expected payoff of the optimal strategy.