The manager of a university bookstore is trying to determine whether or not to advance purchase copies of a popular textbook. Her uncertainty is caused by the changing popularity of the course that requires the book. The table below characterizes the uncertainties as well as the present worths of her options.

The bookstore manager can pay \(\$ 6,000\) for a student survey that will predict whether the course's popularity will go up or down. The table below indicates the results of past predictions using student surveys.

a. Draw a decision tree to represent this situation.

b. Determine whether or not the manager should advance-purchase the textbook or pay for the survey.

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Future Popularity of the Course Probability PW of Savings with Advanced Purchase High 0.5 $200,000 Medium 0.3 -$40,000 Low 0.2 -$150,000