Kroft Food Products is attempting to decide whether it should introduce a new line of salad dressings called Special Choices. The company can test market the salad dressings in selected geographic areas or bypass the test market and introduce the product nationally. The cost of the test market is $150,000. If the company conducts the test market, it must wait to see the results before deciding whether to introduce the salad dressings nationally. The probability of a positive test market result is estimated to be 0.6. Alternatively, the company can decide not to conduct the test market and go ahead and make the decision to introduce the dressings or not. If the salad dressings are introduced nationally and are a success, the company estimates that it will realize an annual profit of $1.6 million, whereas if the dressings fail, it will incur a loss of $700,000. The company believes the probability of success for the salad dressings is 0.50, if they are introduced without the test market. If the company does conduct the test market and it is positive, then the probability of successfully introducing the salad dressings increases to 0.8. If the test market is negative and the company introduces the salad dressings anyway, the probability of success drops to 0.30.
Suppose that the company is suspicious of the conditional probabilities given at the end of the problem description (i.e., the 0.8 and 0.3). Because of these suspicions, the company conducted a study and found the following:
i) In past cases where a product wound up being successful, the test market results were positive with a probability of 0.6
ii) In past cases where a product did not wind up being successful, the test market results were negative with a probability of 0.8
Using the results of the study and Bayes' Theorem, use decision tree analysis to determine the company's optimal strategy.
Please provide the decision tree and Bayes' analysis with explanation.