# Copy Makers Inc. (CMI) has just received a credit request from a new customer who wants to purchase a copying

## Question:

Copy Makers Inc. (CMI) has just received a credit request from a new customer who wants to purchase a copying machine. As input to its decision of whether to grant credit, CMI has made the following estimates and assumptions:

• If CMI denies the customer credit, there is a 20 percent chance that the customer will buy the copying machine with cash anyway.
• If CMI grants credit, there is a 70 percent chance the customer will be a good credit risk.
• If CMI grants credit and the customer is a good credit risk, CMI will collect 100 percent of the purchase price.
• If CMI grants credit and the customer is a bad credit risk, CMI has two options. Under the first option, CMI would continue to send the customer a bill and hope it is eventually paid. Under this option, CMI will collect 100 percent, 50 percent, or 0 percent of the amount owed, with probabilities 0.1, 0.2, and 0.7, respectively. Under the second option, CMI would vigorously pursue the collection of the amount owed. To do so would cost CMI 25 percent of the amount owed, regardless of the amount eventually collected. Under this second option, CMI will again collect 100 percent, 50 percent, or 0 percent of the amount owed, with probabilities 0.3, 0.5, and 0.2, respectively.
• The copy machine sells for \$8,000 and costs CMI \$5,000. Nonvigorous enforcement has no cost, while vigorous enforcement costs \$2,000.

a. What is the complete, optimal decision strategy for CMI?
b. What is the optimal expected value?