Textbook Problem

Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the company’s mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available:

• If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog.
• If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives.
• If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives.
• If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives.
• If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives.
• If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives.

It costs $2 to send a catalog, and the average profit per order is $30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?