Solve and a build a decision tree: 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:

Historically, when CMI denies a customer credit, there is a 20% chance that the customer will buy the copying machine with cash anyway.

If CMI extends credit to a customer, there is an estimated 70% chance the customer will be a good credit risk and pay in full. If CMI grants credit and the customer is a bad credit risk, CMI has two options:

Option 1: CMI would continue to send the customer a bill (at negligible cost) and hope it is eventually paid. Under this option, CMI will collect all, half, or none of the amount owed, with probabilities 0.1, 0.2, and 0.7, respectively.

Option 2: CMI would hire a collections agent at a cost of 25% 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.

Note: if the transaction is not completed, the cost of the copy machine is not "lost" - assume the machine will simply be for the next client.

Questions:

1) What is the optimal decision strategy for CMI?

2) What is the optimal expected value of a customer who wishes to purchase a copying machine?

3) Under these assumptions, at what price threshold (price charged to customer) would CMI change its decision to extend credit to customers? Find the best answer within $10 margin of error.

Show decision tree.