Consider a salesman who has offices in two towns called town 1 and town 2. He can be in one of these towns on any particular day but cannot split his time on any day between the two. On any day that...

Consider a salesman who has offices in two towns called town 1 and town 2. He can be in one of these towns on any particular day but cannot split his time on any day between the two. On any day that he works in town 1, the probability of making a sale is 0.4; similarly, on any day that he is in town 2 the probability that he makes a sale is 0.25. The reward for making any sale is $100, and the cost of switching towns is $50. The salesman is considering two operating alternatives:

a. Stay in each town until he makes a sale and then go to the next town.

b. Work in one town one day and then go to the next town the next day whether or not a sale is made. Define the four possible policies for the problem and find the salesman’s long-run expected profit per day