Mr. D’s Supermarket is determined to please its customers with a customer-advantage card. Currently, 30 percent of all their shoppers are loyal to Mr. D’s. A loyal Mr. D’s customer shops at Mr. D’s 85 percent of the time. A disloyal Mr. D’s customer shops at Mr. D’s 10 percent of the time. A typical customer spends $150 per week, and Mr. D’s is running on a 4 percent profit margin.

The customer-advantage card will cost Mr. D’s an average of $0.01 per dollar spent. You believe Mr. D’s share of loyal customers will increase by an unknown amount between 2 percent and 10 percent. You also believe that the fraction of the time a loyal customer shops at Mr. D’s will increase by an unknown amount between 2 percent and 12 percent. Should Mr. D’s adopt a customer-advantage card? Should Mr. D’s adopt the card if its profit margin is 8 percent instead of 4 percent?