Hale's TV production is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decisions alternatives and profits (in thousands of dollars) are as follows: Decision Alternative State of Nature Reject, s1 1 year, s2 2 years, s3 Produce Pilot, d1 -100 50 150 Sell to competitor, d2 100 100 100 The probabilities for the states of nature are (1 ) = 0.20,(2 ) = 0.30, (3 ) = 0.50. For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chances of a favourable network reaction to the series. Assume that the agency review will result in a favourable (F) or an unfavourable (U) review and that the following probabilities are relevant. () = 0.69,() = 0.31 ( 1 ) = 0.09 ,( 2 ) = 0.26 , ( 3 ) = 0.65 ( 1 ) = 0.45,( 2 ) = 0.39,( 3 ) = 0.16 a. Construct a decision tree for this problem. (2 marks) b. What is the Hale's optimal decision strategy