Problem #1 (25 points) 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 New customer with no history State 2 During most recent call, customer's interest level low State 3 During most recent call, customer's interest level medium State 4 During most recent call, customer's interest level high State 5 Sale completed during most recent call State 6 Sale lost during most recent call Based on past phone calls, the following transition matrix has been estimated: 1 2 3 4 5 6 1 0 .25 .15 20.30 .10 2 0 20.10 20.45.05 3 0 .15 .35 25.10 .15 4 0 .15 .30 30 .05 20 5 0 0 0 0 1 0 6 0 0 0 0 0 1 - au (a) Which states are transient? (b) Which states are absorbing? (c) Calculate (1-0) and (1-0) R. (d) For a customer who is currently having a high degree of interest, determine the average number of calls made before the customer buys the product or the sale is lost. (e) What is the probability that a new customer will buy the product? (f) What is the probability that a customer who is currently having a low level of interest will buy the product? (g) Suppose a call costs $23 and a sale earns $299 in revenue. Determine the "value" of each type of customer. Problem#2 (25 points) Problem #1 (25 points) 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 New customer with no history State 2 During most recent call, customer's interest level low State 3 During most recent call, customer's interest level medium State 4 During most recent call, customer's interest level high State 5 Sale completed during most recent call State 6 Sale lost during most recent call Based on past phone calls, the following transition matrix has been estimated: 1 2 3 4 5 6 1 0 .25 .15 20.30 .10 2 0 20.10 20.45.05 3 0 .15 .35 25.10 .15 4 0 .15 .30 30 .05 20 5 0 0 0 0 1 0 6 0 0 0 0 0 1 - au (a) Which states are transient? (b) Which states are absorbing? (c) Calculate (1-0) and (1-0) R. (d) For a customer who is currently having a high degree of interest, determine the average number of calls made before the customer buys the product or the sale is lost. (e) What is the probability that a new customer will buy the product? (f) What is the probability that a customer who is currently having a low level of interest will buy the product? (g) Suppose a call costs $23 and a sale earns $299 in revenue. Determine the "value" of each type of customer. Problem#2 (25 points)