A manufacturer must decide whether to extend credit to a retailer who would like to open an account.

A manufacturer must decide whether to
extend credit to a retailer who would like to open an account with the firm.
Past experience with new accounts indicates that 45% are high-risk customers,
35% are moderaterisk customers, and 20% are low-risk customers. If credit is
extended, the manufacturer can expect to lose $60,000 with a high-risk
customer, make $50,000 with a moderate-risk customer, and make $100,000 with a
low-risk customer. If the manufacturer decides not to extend credit to a
customer, the manufacturer neither makes nor loses any money. Prior to making a
credit extension decision, the manufacturer can obtain a credit rating report
on the retailer at a cost of $2000. The credit agency concedes that its rating
procedure is not completely reliable. In particular, the credit rating
procedure will rate a low-risk customer as a moderate-risk customer with
probability 0.10 and as a high-risk customer with probability 0.05. Similarly,
the given rating procedure will rate a moderate-risk customer as a low-risk
customer with probability 0.06 and as a high-risk customer with probability
0.07. Finally, the rating procedure will rate a high-risk customer as a
low-risk customer with probability 0.01 and as a moderate-risk customer with
probability 0.05. Find the strategy that maximizes the manufacturer’s expected
net earnings. (Note: If you set up the input section of your spreadsheet in the
right way, you will be able to perform all of the Bayes’ rule calculations with
a couple of copyable formulas.)