Olive Branch is a writer of romance novels. A movie company and a TV network both want exclusive rights to one of her most popular works. If she signs with the network she will receive a single lump sum, but if she signs with the movie company, the amount she will receive depends on the market response (box office) to the movie. Olive's payoffs are summarized:

Box Office

Small Medium Large

Movie Company $200,000 1,000,000 3,000,000

TV network 900,000 900,000 900,000

Probability 0.3 0.6 0.1

1. (5 pts.) Without any additional information, what is Olive's best decision?

Additionally, Olive may hire a market research firm to conduct a survey at a cost of $100,000. The result of the survey would be either a "F"avorable or an "U"nfavorable public response to the movie. The firm's historical accuracy, as measured by conditional probabilities is:

P("F"|Small) = .3 P("U"|Small) = .7

P("F"|Medium) = .6 P("U"|Medium) = .4

P("F"|Large) = .8 P("U"|Large) = .2

b. (5 pts.) Draw the decision tree for this problem

c. (5 pts.) What is Olive's best decision?

d. (5 pts.) What is the most that Olive should be willing to pay for the survey results?