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A telephone sales force can model its contact with customers as a Markov chain. The six...

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Advance Math

A telephone sales force can model its contact with customers asa 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 lowState 5 During most recent call, customer’s interest level mediumState 6 During most recent call, customer’s interest levelhigh
Based on past phone calls, the following transition matrix has beenestimated:
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 madebefore 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 ofinterest 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.

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