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.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 70P

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You have 5 and your opponent has 10. You flip a fair coin and if heads comes up, your opponent pays you 1. If tails comes up, you pay your opponent 1. The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability that you end up with all the money and the probability that neither of you goes broke in 100 tosses.
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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?
If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels. The cost of pesticides is $20,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $10.00 with probability of 0.50 or it will be $12.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $11.00. What will be his total production cost if he uses pesticides? a. $430,000.00 b. $470,000.00 c. $450,000.00 d. $660,000.00
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Consider a population of 3000 people, 1400 of whom are men. Assume that 700 of the women in this population earn at least $60,000 per year, and 500 of the men earn less than $60,000 per year. a. What is the probability that a randomly selected person from this population earns less than $60,000 per year? b. If a randomly selected person is observed to earn less than $60,000 per year, what is the probability that this person is a man? c. If a randomly selected person is observed to earn at least $60,000 per year, what is the probability that this person is a woman?
A car repair can be performed either on time or late, and either satisfactoryily or unsatisfactorily. The probability of a repair being on time and satisfactory is 0.26. The probability of a repair being on time is 0.74. The probability of a repair being satisfactory is 0.41. What is the probabilityof a repair being late and unsatisfactory?
Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] Which of them has a σ of 9 using the probability model approach. a) [12.5968, 2, -2 and -12.5968] B) [12.5968, 4, -2 and -12.5968]

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