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Problem 3, Page 953

New York City produces 1,000 tons of air pollution per day, Jersey City 100 tons, and Newark 50 tons. Each day, ⅓ of New York’s pollution is blown to Newark, ⅓ dissipates, and ⅓ remains in New York. Each day, ⅓ of Jersey City’s pollution is blown to New York, ⅓ stays in Jersey City, and ⅓ is blown to Newark. Each day, ⅓ of Newark’s pollution stays in Newark, and the rest is blown to Jersey City. On a typical day, which city will be the most polluted?

Transition Matrix:





New York(NY)

Newark (NW)

Dissipate

Jersey (J)

New York(NY)

1/3

1/3

1/3

0

Newark (NW)

0

1/3

0

2/3

Dissipate

0

0

1

0

Jersey (J)

1/3

1/3

0

1/3

1000-2/3NY+1/3J = 0

50-2/3NW+1/3NY+1/3J = 0

100-2/3J+2/3NW = 0 +

1150 = 1/3NY

NY= 3450

1000-2/3(3450)+1/3J = 0

J = 3900

300-2(3900)+2NW = 0



NW = 3750




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