Question: Decision Tree Model ( 3 0 points):

The executives of the General Products Company (GPC) have to decide which of three products to introduce, A, B, or C. Product C is essentially a risk-free proposition, from which the company will obtain a net profit of $1 million. Product B is considerably more risky. Sales may be high, with resulting net profit of $8 million, medium with net profit of $4 million, or low, in which case the company just breaks even. The probabilities for these outcomes are:

P (Sales High for B) = 0.38

P (Sales Medium for B) = 0.12

P (Sales Low for B) = 0.50.

Product A poses some difficulty; a problem with the production system has not yet been solved. The engineering division has indicated its confidence in solving the problem, but there is a slight chance (5%) that devising a workable solution may take a long time. In this event, there will be a delay in introducing the product, and that delay will result in lower sales and profits. Another issue is the price for Product A. The options are to introduce it at either high or low price; the price would not be set until just before the product is introduced. Both of these issues will affect the ultimate net profit.

Finally, once the product is introduced, sales can be either high or low. If the company decides to set a low price, then low sales are just as likely as high sales. If the company sets a high price, the likelihood of low sales depends on whether the product was delayed by the production problem. If there is no delay and the company sets a high price, the probability is 0.4 that sales will be high. But if there is a delay and the price is set high, the probability is only 0.3 that sales will be high. The following table shows the possible net profit figures for Product A:

Please frame the problem in a decision tree model and find the optimal strategies. You need to construct the decision tree and provide it to show your procedures of solving the problem.

( HINT : There is no need to calculate the posterior probabilities)

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Solution: The downloadable solution consists of 2 pages
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