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# homewk4 - IEOR 4106 Introduction to Operations Research...

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IEOR 4106: Introduction to Operations Research: Stochastic Models Spring 2009, Professor Whitt Homework Assignment 4: Tuesday, February 10 Due on Tuesday, February 17. To be discussed at the recitation on Sunday, February 15. Even More Markov Chains Read Sections 4.5.1, 4.5.2, 4.6 and 4.8 (pages 236-242; 232-238 in 8th ed., up to Example 4.33) in Ross. Do the following exercises at the end of Chapter 4. (Again the numbering is the same in the 8th and 9th editions.) Turn in all except for ones with answers in back: 41. (Answer in back) 42. 46. 47. (Answer in back) 49. 56. (Hint: Apply Section 4.5.1.) 57. ( Hint: Apply Section 4.5.1 again.) 76. Explanation and hint: We consider a graph in which the nodes are the 64 squares of the chess board. Let an arc join nodes i and j if a knight can move from i to j in one move. Recall that a knight moves two squares in one direction (horizontally or vertically) and one square in another direction (horizontally or vertically), not allowing both horizontal or both vertical. We also use Remark (ii) in Section 4.4 about the relation between

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homewk4 - IEOR 4106 Introduction to Operations Research...

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