Anita Campos, a vice president in High Place's Studio's production-finance department, had to make a recommendation to

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Question:

Anita Campos, a vice president in High Place's Studio's production-finance department, had to make a recommendation to the studio's president, Leah Walsh, regarding whether to go ahead with the production of an exciting new movie mystery. This new movie idea was risky - it could become a blockbuster hit or it could be a costly failure.

Campos could recommend producing a different movie script, a Western-themed drama for release on Home Box Office (HBO), which promised fairly certain profits. However, a movie theater release would provide more prestige and profit for the studio if the film were a hit, but also had the potential for significant losses if the movie failed.

High Places Studio was a young studio with only enough resources to produce one of these films.

The HBO option virtually guaranteed profits of $3 million.

The choice depended on some key factors:

The first step was choosing a good script. The studio already had one that they like, Tuna on Rye, a mystery set in Brooklyn. A popular actor, Nick Petty, had already signed on for the lead role, which was a promising start for this movie. The alternative would be to go with the HBO Western drama, for which the studio already had the necessary resources (they would not need to find a director).

A crucial factor if the studio chose to produce Tuna on Rye was the choice of director. The studio was in discussions with two directors:

One was Max Morgan, one of the best known directors in Hollywood. Morgan was interested and would take the job if offered it, as long as his schedule allowed. He was still working on another film, and there was only a 70% chance that he would be able to direct. The total cost for a Morgan-directed film would be $60 million. Morgan also had a reputation for not finishing films on time. If the film was completed late, a 40% probability, Campos estimated only $30 million in revenues. Instead of releasing a film late, the studio could just abandon the film after spending only 75% of the total costs. If the film was completed on time, there was a 20% chance of it being a "blockbuster," bringing in $180 milling in revenues, a 50% chance of being a "hit," bringing in $80 million in revenues, and a 30% chance of being a "miss," bringing in only $35 million in revenues.

If Morgan could not direct, the Campos had already lined up Maggie McManus to direct. The total cost for a McManus-directed film would be $35 million. In the past, her films were always completed on time, so there was no concern about a late release. However, McManus was not as well-known as Morgan, so the revenue possibilities were lower. A McManus film was equally likely to be a "hit," bringing in $45 million in revenue, or a "miss," bringing in $30 million in revenue, but no chance of being a "blockbuster."

In this problem, you will build decision trees to help Anita Campos make her recommendation to the studio president. This problem has three parts, where you will model the situation described above, and then look at the value of control and the value of perfect information.

You may create separate trees for each, but you will need to upload them all in the same file.