A telephone sales force can model its contact with customers as a Markov chain. The six states of the chain are as follows:
State 1 Sale completed during most recent call
State 2 Sale lost during most recent call
State 3 New customer with no history
State 4 During most recent call, customer’s interest level low
State 5 During most recent call, customer’s interest level medium
State 6 During most recent call, customer’s interest level high
Based on past phone calls, the following transition matrix has been estimated:
a For a new customer, determine the average number of calls made before the customer buys the product or the sale is lost.
b What fraction of new customers will buy the product?
c What fraction of customers currently having a low degree of interest will buy the product?
d Suppose a call costs $15 and a sale earns $190 in revenue. Determine the “value” of each type of customer.