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

Question

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 I'm pretty sure we must 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

Let us calculate the expected profit = 0.4*750,000 - 0.6*450,000 = 30000

The total cost of administering the survey should not exceed 30,000 in order not to incur losses. So if the cost of survey is C, let us find out what is the expected favourable out of it

[0.4*(0.6-0.1) + 0.6(0.1 - 0.7)]C > -30,000

i.e C < 30,000/(0.16)

Hence any value less than 30,000/0.16 can be put on survey

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