For problem 15-26, suppose that the designer can obtain some expert advice for a cost of $30,000. If the fashion is going to be short, there is a 0.90 probability that the expert will predict short, a 0.05 probability that the expert will predict medium, and a 0.05 probability that the expert will predict long. If the fashion is going to be medium, there is a 0.10 probability that the expert will predict short, a 0.75 probability that the expert will predict medium, and a 0.15 probability that the expert will predict long. If the fashion is going to be long, there is a 0.10 probability that the expert will predict short, a 0.10 probability that the expert will predict medium, and a 0.80 probability that the expert will predict long. Construct the decision tree for this problem. What is the optimal decision for the designer?

Problem 15-26

Predicting the styles that will prevail in a coming year is one of the most important and difficult problems in the fashion industry. A fashion designer must work on designs for the coming fall long before he or she can find out for certain what styles are going to be "in." A well-known designer believes that there is a 0.20 chance that short dresses and skirts will be popular in the coming fall; a 0.35 chance that popular styles will be of medium length; and a 0.45 chance that long dresses and skirts will dominate fall fashions. The designer must now choose the styles on which to concentrate. If she chooses one style and another turns out to be more popular, profits will be lower than if the new style were guessed correctly. The following table shows what the designer believes she would make, in hundreds of thousands of dollars, for any given combination of her choice of style and the one that prevails in the new season.

Construct a decision tree, and determine what style the designer should choose to maximize her expected profits.