This problem is found in the chegg textbook solutions here, https://www.chegg.co

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This problem is found in the chegg textbook solutions here, https://www.chegg.com/homework-help/-5th-edition-chapter-6-problem-52P-solution-9781133588269, but uses decision tree software and the decision tree images cut off and are unclear. Note: I've seen the two related questions on this problem that were already answered, but I'm concerned about their correctness/methods. For my class, we must set up a decision tree, and use Bayes' theorem to solve.

A company is considering whether to market a new product. Assume, for simplicity, that if this product is marketed, there are only two possible outcomes: success or failure. The company assesses that the probabilities of these two outcomes are p and 1 - p, respectively. If the product is marketed and it proves to be a failure, the company will have a net loss of $450,000. If the product is marketed and it proves to be a success, the company will have a net gain of $750,000. If the company decides not to market the product, there is no gain or loss. The company is also considering whether to survey prospective buyers of this new product. The results of the consumer survey can be classified as favorable, neutral, or unfavorable. In similar cases where proposed products were eventually market successes, the fractions of cases where the survey results were favorable, neutral, or unfavorable were 0.6, 0.3, and 0.1, respectively. In similar cases where proposed products were eventually market failures, the fractions of cases where the survey results were favorable, neutral, or unfavorable were 0.1, 0.2, 0.7, respectively. The total cost of administering this survey is C dollars.

Let p=0.4. For which values of C, if any, would this company choose to conduct the consumer survey?

For this problem, how would you solve the bolded question by hand?

Explanation / Answer

The thing to remember here is that the company will go for the survey, only if its expected profit is atleast equal to the cost of conducting the survey.

This means that it is not economically feasible to conduct the survey, if the expected profit is not sufficient to cover the cost of the survey.

From given data, we have:

Expected profit = p * 750,000 + (1-p) * (-450,000)

= 1,200,000p - 450,000

For p=0.4, The expected profit comes out to be 30,000

Thus, the cost of conducting the survey (C) should be at most 30,000 dollars.

i.e. C should be between $0 and $30,000

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