In an office complex of 1180 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 84% chance that she will be at work tomorrow, and if the employee is absent today, there is a 64% chance that she will be absent tomorrow. Suppose that today there are 991 employees at work. (a) Find the transition matrix for this scenario (assume that state 1 is "at work" and state 2 is "absent"). (b) Predict the number that will be at work five days from now. (c) Find the steady-state vector. (Note that the sum of the entries must be the total number of employees, but make sure that your answers are correct to at least 1 decimal place.)

In an office complex of 1180 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 84% chance that she will be at work tomorrow, and if the employee is absent today, there is a 64% chance that she will be absent tomorrow. Suppose that today there are 991 employees at work. (a) Find the transition matrix for this scenario (assume that state 1 is "at work" and state 2 is "absent"). (b) Predict the number that will be at work five days from now. (c) Find the steady-state vector. (Note that the sum of the entries must be the total number of employees, but make sure that your answers are correct to at least 1 decimal place.)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 55E

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