Question

Question B6 A soft drink company is going to develop a new flavor of soft drink so as to maximise its profit The new flavor is either mango (d) or pineapple (d). The sales of the new flavored soft drink depend on the demand of the market which is either low (si) or high (52). Estimated profits (in millions HKS) and probability assessments of low and high demands are as follows: Decision Alternative Mango flavor, d Pineapple flavor, d P(s) State of Nature low demand, si high demand, 90 100 7 0 1 20 0.6 0.4 Mango (a) Find the expected value of perfect information (EVPI). (3 marks) Before making the decision, the manager of the soft drink company is considering doing a market research to gather more information about the demand of the market. The outcome of the market research will either be favorable (F) or unfavorable (U). The manager then constructed the following decision tree with relevant probabilities. Low demands .90 P(S1IF) = 0.9 flavor, di High demand, 8 100 Favorable, F P(F) = 0.4 Low demand, 70 Pineapple P($11F) = 0.9 flavor, de High demand, 8 120 Low demand, s 00 P(S1\U) = 0.4 flavor, di High demand, $ 100 Unfavorable, U P(U) = 0.6 L Low demand, 5 20 Pineapple 10P( SU) = 0.4 flavor, d? High demand, 120 Mango 9 (b) Find the expected value (EV) of node 4 of the decision tree. (Correct your final answers to 2 decimal places) (4 marks) (c) Find the expected value of sample information (EVSI). (Correct your final answer to 1 decimal place) (2 marks) (d) Construct a risk profile (in a table) for the optimal decision strategy. (Correct your final answers to 2 decimal places whenever appropriate) (3 marks)

please including the steps of each question

Answer 1

that a soft drink in Jerry to inclop a Given nee love of Soft drink Soos movimie 10 Profit either mango (di) or fireapple (dy) The new flavora is The sales of the on the demand of or high (52) new flavored soft darink the market which is deperd either low (s) I find the expected value of Doolfect information (EPI) EVPL = EPPY - Emy* perfect information EPPI is the expected profit with and Emrt is the maximum EMV Low demanasi) High demand (S2) | ao 100 mango flavor (a) to In Pineapple flavoor (ody PCs:) (p=1,2) 0.6

land let the m w Moyorir Capaciteit Zwice, How Miopi (ty) Enn is monimum for mange floor 94 caut eppi Tabale to is given find below LOW THigh demand demand (S1) (8) Expected pay off under perfect information mango flavored, 54 48 Pineapple flavor (22) 48 0:4 Eppi = 102 Pesi)

information value of prefecih Expected 02- 94 EVPI u of the b find the expected value (Ev) of node decision tree tree decision in the 4 of node value Expected Profit Expected Potit. 364 mango Low (Prob=0.0 90 High (prob= 0.1) 100 Low (Prob- og to High (proba 0:0) 120 F (Proba 0:4) Pineapple mango Low (Prob=1.4 High (Pro6=0.6 Low Prob 20:4 Heigh (prob: 0.6 90 100 70 120 Lul Prob: 0.6 Pineapple

Hence ev of node u is 264AGO 5964 of sample information expected value - find the CEVSD Erst is (Accurate 94 (Refor a Information & cost of information) - In accurate Inform- d risk Profile for the optimal decision Construct a Strategy 96.4 Refer b.