Represent the situation as a Markov chain. Determine the probability that the professor will purchase the current model (M1, M2, M3) in 4 years. An engineering professor acquires a new computer once every 2 years. The professor can choosefrom three models: M1, M2, and M3. If the present model is M1, the next computer can be M2 withprobability .2, or M3 with probability .15. If the present model is M2, the probabilities of switching toM1 and M3 are .6 and .25, respectively. And, if the present model is M3, then the probabilities ofpurchasing M1 and M2 are .5 and .1, respectively.

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Answered: An engineering professor acquires a new…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.4: Marketing Models

Problem 29P

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|At the Pleasant Haven Hotel there are 36 rooms. The profit earned when a room is sold for a night is $53. If Pleasant Haven overbooks, by selling more reservaitions than they have rooms and they end up having a customer whose reservation cannot be fulfilled, the loss to Pleasant Haven is $30 for that customer. Regardless of the number of rooms booked, the probability of one no show is 60% and the probability of 2 no shows is 20%. There is zero probability of more than 2 no shows. For a night when requests are exceeding the 36 rooms, what is the optimal number of reservations to accept? Assume there is no penalty for a customer who does not show up, i.e., Pleasant Haven does not make $53 on a customer that is a no show. What is the expected net for booking each of the following: (Net means profit minus any overbooking loss.) 36 customers 37 customers 38 customers What is the best number of book?
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