A manufacturer is trying to choose between two production methods (a1 and a2) fo

Question

A manufacturer is trying to choose between two production methods (a1 and a2) for a new product. He considers that the probability of demand for the new product being good (s1) is 0.4 and the probability that demand will be poor (s2) is 0.6. In evaluating the two production methods the manufacturer has calculated the following table of conditional profits:

(a) Which production method should be used? Show calculations.

The manufacturer asks a marketing consult for an opinion as to whether demand will be good or poor. From previous experience when the consultant has indicated that demand will be good she has been right 80% of the time, and when she has indicated that demand will be poor she has been right 70% of the time.

(b) Revise the prior probabilities in light of the consultant’s track record.

(c) What is the posterior probability of good demand given that the consultant has indicated demand will be good?

(d) What is the expected net gain or loss from engaging the consultant? Should the consultant be engaged? Why?

Explanation / Answer

a1 productions

Good=$24,000 * 0.4=$9,600

Poor=$15,000*0.6=$9,000

a2 productions:

Good=-$4,000 *04= -$1,600

Poor=$$40,000*0.6=$24,000

Selection is a1 is better than a2 because a1 does not having negative of the good like a2 at the same time a2 bad probability amount is high.

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b)prior probabilities:

Good

=1.2(0.4+0.8)/1

=1.2

Bad:

=0.6+0.7/1

=1.3

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c)posterior probability

Good=1.2 *0.8/1

=0.16

Bad=1.3*0.7/1

=0.91

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d) There is no use for engaging the consultant because manufacturer itself calculated same as consultant.

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