Hale$$s Productions is considering producing a pilot for a comedy series in the hope of$$selling it to a major streaming service. The streaming service 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 streaming$$service$$s decision or transfer the rights for the pilot and series to a competitor for$$$$100,000.$ Hale$$s decision alternatives and profits $($in thousands of dollars$)$ are as$$follows:$$State of Nature$$Decision Alternative Reject, s$11$ Year, s$22$ Years, s$3$Produce pilot, d$110050150$Sell to competitor, d$2100100100$The probabilities for the states of nature are P$($s$1)=0\mathrm{.}20,$ P$($s$2)=0\mathrm{.}30,$ and P$($s$3)=0\mathrm{.}50.$For a consulting fee of $$5000,$ an agency will review the plans for the comedy series and$$indicate the overall chances of a favorable streaming service reaction to the series.$$Assume that the agency review will result in a favorable $($F$)$ or an unfavorable $($U$)$ review$$and that the following probabilities are relevant.$$P$($F$)=0\mathrm{.}69$ P$($s$1|$ F$)=0\mathrm{.}09$ P$($s$1|$ U$)=0\mathrm{.}45$P$($U$)=0\mathrm{.}31$ P$($s$2|$ F$)=0\mathrm{.}26$ P$($s$2|$ U$)=0\mathrm{.}39$P$($s$3|$ F$)=0\mathrm{.}65$ P$($s$3|$ U$)=0\mathrm{.}16$a$.$ Construct a decision tree for this problem.$$b$.$ What is the recommended decision if the agency opinion is not used? What is the$$expected value?$$c$.$ What is the expected value of perfect information?$$d$.$ What is Hale$$s optimal decision strategy assuming the agency$$s information is used?$$e$.$ What is the expected value of the agency$$s information?$$f$.$ Is the agency$$s information worth the $$5000$ fee? What is the maximum that Hale$$should be willing to pay for the information?$$g$.$ What is the recommended decision?