Question 3

A shop owner is attempting to decide whether to purchase a new machines (A, B and C) to attract new customers. The profit or loss from each purchase and the probabilities associated with each purchase outcome are shown in the following payoff table:

a. Compute the expected value for each purchase and select the best one.

b. Using decision criteria, determine the best investment (if you need assumptions, please do it).

c. You are now considering hiring a consultant to see if the shop will get the new contract from other costumers. The owner has estimated that a .70 probability that the consultant would present a favourable report, given that the contract is awarded, and a .80 probability that the consultant would present an unfavourable report, given that the contract is not awarded. Based on this, please discuss what is Bayesian analysis (or Bayes’ theorem) and how Bayesian analysis can be used to solving this problem? Using decision tree analysis and posterior probability tables, determine the decision strategy the company should follow, the expected value of the strategy, and the maximum amount the company should pay the consultant.