For the purposes of this decision exercise, the government focuses on Type 2 of the intentional and economically-motivated food fraud: deliberate mislabelling. The decision will be made on a financial basis. Assume each container accepted to enter the country and brings fraudulent food products costs the government 200,000 and each container that enters the country and does not have any fraudulent food products contributes 25,000 to the national economy. Assume that 10% of all potential containers to enter the country has fraudulent food products. The government may admit all containers, no containers, or test containers for fraudulent food products before determining whether they should be admitted. It costs 10,000 to test a container for fraudulent food products; and the test result is either positive or negative. When the test result is positive, then the container has fraudulent food products 95% of the time. However, 15% of all containers that have fraudulent food products test negative. A container that does not have any fraudulent food products tests negative 99.6% of the time. The government's goal is to maximise per potential container the expected benefits minus the expected costs.

a. Use a decision tree analysis to aid the government on their testing policy. Hint: Expecting a sequential decision analysis with probabilities estimated using the Bayes' Rule.

b. Calculate the Expected Value of Perfect Information and the Expected Value of Sample Information. Interpret your results.

c. Under what circumstances would this approach be preferable?