answer the question

The Director of Logistics of a textile firm is in charge of deciding between buying a new electric forklift truck costing $25,000 or a second -hand 10 -year -old costing $12,500, to handle textile parts weighing up to 2,100 kg and for a height of up to 4 m. The maintenance costs of a new forklift truck for the next 10 years are estimated at $1,000, whereas the costs of maintaining a second -hand truck are expected to double those of a new one. Evidently if the second -hand forklift truck operates properly, it entails a saving of $11,500, but if it is faulty, it will entail losing the money spent on not only purchasing it, but also on the purchase and maintenance of a new model. Evidently, the Dir ector will be reprimanded by the Manager. Based on the statistical data provided by the seller, the Director of Logistics has established that the proportion of faulty second -hand equipment is 20 % and that the reliability of a new forklift truck is consid ered 100 %. Before purchasing a second -hand forklift truck, two types of mechanical and electric tests can be done: • TEST A: at a cost of $1,000, whose diagnosis offers a percentage of failures of 5 % if it is faulty, and of 20 % if it operates properly. • TEST B: consists in two successive phases. In the first one, whose cost is $800, a preliminary diagnosis can be made whose probability of error is 15 %. The second phases entail deciding whether to buy or reject the forklift truck, or to complete the tes t, which costs a further $700, in order to be absolutely sure about the state the equipment is in. (a) Draw the corresponding decision tree and indicate with a letter per branch the associated probability or the associated cost (depending on the case) (b) Solve the decision tree and obtain the most economic decision. (c) What is the imperfect information value for each test? How much does perfect information cost?