Chemco Corporation is a chemical company. The research and development manager is trying to decide whether or not to develop a new solvent that would work at all conditions. It is thought that the solvent project may be a major success with an estimated value of $1,500,000, a moderate success with an estimated value of $800,000 since it can be sold to another company to help with its current project, or a total failure. If the project is a failure, it will cost the company $700,000. Based on the subjective judgment of the manager, the following probabilities are assigned to the three possibilities.

P(major success) = 0.20

P(moderate success) = 0.40

P(failure) = 0.40

The company is also considering consulting an expert from a research institution to study the project for a fee of $30,000. The expert will develop a prototype solvent to determine if it would work at all temperatures. Based on previous experience with the expert, the following conditional probabilities are realistic appraisals of the expert's evaluation accuracy.

P(prototype works | major success) = 0.9

P(prototype works | moderate success) = 0.6

P(prototype works | failure) = 0.3

1) What is the recommended decision if the expert is not used? What is the expected value?

2) What is the expected value of perfect information? Explain what it means.

3) Construct a decision tree for this problem, and determine all probabilities. What is the optimal decision strategy and its expected value?

4) What is the maximum amount the company should be willing to pay to the expert?

2. A product manager for a soap manufacturer must decide whether or not to offer a new, biodegradable laundry detergent. The projected profit from a successful detergent is $2 million, whereas failure of the product would result in a loss of $1 million. The manager currently thinks there is a 40% chance that the product will be successful. Not offering the product would not change profits.

At a cost of $100,000, the product can be tested. Consumer testing can be favorable, a 50% chance, or unfavorable. Given a favorable test result, the chance of product success is judged to be 80%. However, for an unfavorable test result, the chance of product success is judged to be only 30%.

Construct a decision tree for this problem. What is the optimal decision strategy and its expected value? Compute the manager's expected value of sample information (EVSI) and explain what it means. What is the manager's expected net gain of sample information (ENGSI)?