Question

Scholastic Publishing Company received a six-chapter manuscript for a new college text-book. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the textbook will be successful. If successful, a profit of $750,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $250,000 will occur.

Before making the decision to accept or reject the manuscript, the editor can also send the manuscript out for review (cost $5000). A review process provides either a favorable or unfavorable evaluation of the manuscript. Based on past experience the editor knows that 80% of the successful books and 50% of the unsuccessful books had received favorable evaluations.

Must be done in excel.

1. Construct a decision tree for the above decision problem.
2. Analyze the decision tree to determine the optimal decision strategy for the publishing company.
3. Suppose the review is considered “perfect.” What is the most that Scholastic should pay for it?
4. What is the most Scholastic should pay for the current (imperfect) review process?

Answer 1

Construct a decision tree.

Decision tree is a sequential tool that is represented in the form of a graph. It helps the management in the process of decision-making over a period of time.

Decision tree for this problem is as follows:

Analyze and determine the optimal decision strategy.

Expected value of node G:

It is given that the probability of is 0.75 and is 0.25.

Now, calculate the expected value of node G as follows:

Expected value of node H:

It is given that the probability of is 0.417 and is 0.583.

Now, calculate the expected value of node H as follows:

Justification:

• Accept node G (decision) with the expected value of 500.

• Accept node H (decision) with the expected value of 167.

Hence, it is recommended to accept the manuscript whether the review outcome is favorable or unfavorable.

Recommendation:

The manuscript review could not be change the decision to accept. Hence, it is recommended to the company that the manuscript should be reviewed.

Expected value for the perfect information:

In general, the expected value for the perfect information is as follows:

Where,

EVSI be the expected value of perfect information.

EVwPI be the expected value with perfect information about the states of nature.

EVwoPI be the expected value without perfect information about the states of nature.

Expected value with perfect information:

Expected value for the perfect information:

The calculated expected value with perfect information is $487.50 and expected value without perfect information is 400.

Now, calculate the expected value for the perfect information as follows:

Hence, the calculated expected value for the perfect information is 87.5 or $87,500.

Justification:

It is recommended to the company that the better procedure will be helpful for assessing the market potentiality.