P772-4-Indradjaja - 21 January 2008 IE 417 Prof Parisay...

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21 January 2008 IE 417 Prof. Parisay Hwk #4 Parisay’s comments are in red. Pg. 772 #4 ( completed with previous solutions and utility function ) The NBS television network earns an average of \$400,000 from a hit show and loses an average of \$100,000 on a flop. Of all shows reviewed by the network, 25% turn out to be hits and 75% turn out to be flops. For \$40,000, a market research firm will have an audience view a pilot of a prospective show and five its view about whether the show will be a hit or a flop. If a show is actually going to be a hit, there is a 90% chance that the market research firm will predict the show to be a hit. If the show is actually going to be a flop, there is an 80% chance that the market firm will predict the show to be a flop. Determine how the network can maximize its expected profits. Solve using WinQSB. Calculate EVPI and EVSI. Write a report to a manager and explain all your findings. Use utility function for a risk-neutral person and solve using WinQSB. P(S i ) P(Q j | S i ) P(S i | O j ) P(O j ) P(S i | O j ) Probability Probability "given that" Joint Probability P(outcome) P(Posterior) P(H) = .25 P(AH | H)= .9 P( AH and H)= P(H)P(AH|H)= .225 P(AH)= P(AH and H)+P(AH and F)= .375 P(H | AH)= P(H and AH)/P(AH)= . 6 P(F) = .75 P(AF | H)= .1 P( AF and H)= P(H)P(AF|H)= .025 P(AF)= P(AF and H)+P(AF and F)= .625 P(F | AH)= P(F and AH)/p(AH)=.4 P(AH | F)= .2 P( AH and F)= P(F)P(AH|F)= .15 P(H | AF)= P(H and AF)/P(AF)=.0 4 P(AF | F)= .8 P( AF and F)= P(F)P(AF| F)= .6 P(F | AF)= P(F and AF)/P(AF)=.9 6 1

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