When a tennis player serves, he gets two chances to serve in bounds.If he fails to do so twice, he loses the point. If he attempts to serve an ace, heserves in bounds with probability 38. If he serves...

When a tennis player serves, he gets two chances to serve in bounds.If he fails to do so twice, he loses the point. If he attempts to serve an ace, heserves in bounds with probability 38. If he serves a lob, he serves in bounds withprobability 78. If he serves an ace in bounds, he wins the point with probability23. With an inbounds lob, he wins the point with probability 13. If the cost is3+1 for each point lost and -1 for each point won, the problem is to determinethe optimal serving strategy to minimize the (long-run) expected average costper point.(a) Formulate this problem as a Markov decision process by identifying thestates and decisions and then finding the Cik and pij (k) for all decisionsk.(b) Use the policy improvement algorithm to find an optimal policy