STAT379 OPERATIONS RESEARCH II Practical Problems for Week 5 Tutorial SELECTED SOLUTIONS
Practical Problem 1

a) i) P(Beach next year | Beach this year)=0.8 P(Mountains this year | Beach this year)=0.2 b) i) P(Beach in two years | Beach this year)=0.72 P(Mountains in two years | Beach this year) = 0.28

a) ii) P(Beach next year Mountains this year)=0.4 P(Mountains next year Mountains this year) = 0.6

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b) ii) P(Beach in two years time | Mountains this year)=0.56 P(Mountains in two years | Mountains this year) = 0.44

c) Tried three different initial state vectors and all converged to the same long run probabilities (see next page). The long run probability of you going to the beach is 0.66667 and the long run probability of you going to the mountains is 0.33333 which are 2/3 and 1/3 rounded to 5 decimal places.

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Practical Problem 2 a)

P(Purchasing Brand B four purchases from now|equally likely to purchase each brand initially)=0.36275 P(Purchasing Brand C four purchases from now|equally likely to purchase each brand initially)=0.33586

P(Purchasing Brand A four purchases from now|equally likely to purchase each brand initially)=0.30141 2

Output for b), c) and d) respectively.

b) Look at printout in first column of table. P(Purchase Brand A after 4 purchases | purchased brand A this time) =0.6808, P(Purchase Brand B after 4 purchases | purchased brand A this time) =0.29396, P(Purchase Brand C after 4 purchases | purchased brand A this time) =0.02525.

c) Look at second column printout. P(Purchase Brand A after 4 purchases | purchased brand B this time) =0.15203 P(Purchase Brand B after 4 purchases | purchased brand B this time) =0.68837 P(Purchase Brand C after 4 purchases | purchased brand B this time) =0.1596. d) Look at third column output.’ P(Purchase Brand A after 4 purchases | purchased brand C this time) =0.07141 P(Purchase