Problems

1. Whirlswim Appliance is considering giving each of its customers free maintenance on each VCR purchased. They estimate that this proposal will require them to pay an average of $2.50 for each VCR sold today (the cost in today’s dollars). Currently, the market consists of 72,000 consumers whose last purchase was from Whirlswim and 86,000 consumers whose last purchase was from a competitor. In a given year, 40 percent of all consumers purchase a VCR. If their last purchase was a Whirlswim, there is a 60 percent chance that their next purchase will be a Whirlswim. If their last purchase was not a Whirlswim, there is a 30 percent chance that their next purchase will be a Whirlswim. A purchase during the current year will lead to a $20 profit. The contribution to profit (and maintenance cost per purchaser) from a purchaser grows at 5 percent per year. Profits (over a 30- year horizon) are discounted at 10 percent per year.

   Suppose that we provide free maintenance. If the customer’s last purchase was a Whirlswim, the probability that their next purchase will be a Whirlswim will increase by an unknown amount between 0 percent and 10 percent. Similarly, if we give free maintenance and the customer’s last purchase was not a Whirlswim, the probability that their next purchase is a Whirlswim will increase by an unknown amount between 0 percent and 10 percent. Do you recommend that Whirlswim adopt the free maintenance policy?

2. Mr. D’s Supermarket is determined to please its customers with a customer advantage card. Currently, 30 percent of all shoppers are loyal to Mr. D’s. A loyal Mr. D’s customer shops at Mr. D’s 80 percent of the time. A non-loyal 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. We believe Mr. D’s share of loyal customers will increase by an unknown amount between 2 percent and 10 percent. We 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?