346Chapter17HWSolutions

346Chapter17HWSolutions - Chapter 17 Markov Processes...

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Chapter 17 Markov Processes Learning Objectives 1. Learn about the types of problems that can be modeled as Markov processes. 2. Understand the Markov process approach to the market share or brand loyalty problem. 3. Be able to set up and use the transition probabilities for specific problems. 4. Know what is meant by the steady-state probabilities. 5. Know how to solve Markov processes models having absorbing states. 6. Understand the following terms: state of the system transition probability state probability steady-state probability absorbing state fundamental matrix 17 - 1
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1. State Large Probability 0 1 2 3 4 5 6 7 8 9 10 n π 1 ( n ) 0.5 0.55 0.585 0.610 0.627 0.639 0.647 0.653 0.657 0.660 0.662 2/3 π 2 ( n ) 0.5 0.45 0.415 0.390 0.373 0.361 0.353 0.347 0.343 0.340 0.338 1/3 Probabilities are approaching π 1 = 2/3 and π 2 = 1/3. 2. a. Red Pop Red Pop Red Pop Red Pop Super Cola Super Cola Super Cola .9 .9 .9 .1 .1 .1 (.9)(.9) = .81 (.9)(.1) = .09 (.1)(.1) = .01 (.1)(.9) = .09 b. π 1 = 0.5, π 2 = 0.5 c. P = 0 90 010 010 085 . . . . L N M O Q P π 1 = .6, π 2 = .4 3. a. 0.10 b. π 1 = 0.75, π 2 = 0.25 4. a. π 1 = 0.92, π 2 = 0.08 b. Without component: Expected Cost = 0.25 ($500) = $125 With component: Expected Cost = 0.08 ($500) = $ 40 Breakeven Cost = $125 - $40 = $85 per hour. 5.
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346Chapter17HWSolutions - Chapter 17 Markov Processes...

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