Richardson Electronics must decide whether to manufacture an LCD screen at its B

Question

Richardson Electronics must decide whether to manufacture an LCD screen at its Birmingham, AL plant or purchase the screen from a supplier. The resulting profit is dependent on the demand for the product. The payoff table below shows the projected profit in thousands of $. The state of nature probabilities are: P(s1)=.30, P(s2)=.35, P(s3)=.35 Richardson is considering doing a market research study of product demand. They expect the report to be Favorable (F) or Unfavorable (U). From experience they know the following conditional probabilities, Use Bayes theorem to find the revised probabilities for s1, s2, s3. What is the probability of a Favorable and Unfavorable study? Use the tree below to recommend a decision strategy to Richardson.

Explanation / Answer

a. Bayes theorem for finding the revised probabilities of states s1, s2 and s3

Given P(F/s1) =.6 P(F/s2) = .4 and P(F/s3) = .9 similarly P(U/s1)=.4, P(U/s2)=.6 and P(U/s3)=.1

As per formula for joint probabilities P(F.s1) = P(s1).P(F/s1) = P(F).P(s1/F) =.3*.6 =.18

                                                   P(F.s2) = P(s2).P(F/s2) = P(F).P(s2/F) =.35*.4 =.14

                                                    P(F.s3) = P(s3).P(F/s3) = P(F).P(s3/F) =.35*.9 =.315

Similarly all joint probabilities are calculated as follows:

The complete table with posterior probabilities as s/F and s/U for favourable and unfavorable reports are as follows:

From the above calculations it is concluded that the Probability of Favorable report is .635 and Probability of unfavorable report is .365

For decision to manufacture payoff is 100*.3 +40*.35 +(-20)*.35 = 37

For decision to purchase payoff is 70*.3 +45*.35+ 10*.35 = 40.25

Therefore between the alternatives of manufacture and purchase, based on the above expected payoff with given probabilities of likely states of high, medium or low demands, decision is to go for purchase.

P(s) F/s fs U/s us s1 0.3 0.6 0.18 0.4 0.12 s2 0.35 0.4 0.14 0.6 0.21 s3 0.35 0.9 0.315 0.1 0.035 0.635 0.365

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