Question

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:
1100000 20 1 0 0 0 0 3 0.10 0.30 0 0.25 0.20 0.15
P  4 0.05 0.45 0 0.20 0.20 0.10
5 0.15 0.10 0 0.15 0.25 0.35
6 0.20 0.05 0 0.15 0.30 0.30 
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 high degree of interest will buy the
product?
d) Suppose a call costs 20 TL and a sale earns 200 TL in revenue. Determine the “value”
of each type of customer.

Answer 1