In an office complex of 1110 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 77% chance that she will be at work tomorrow, and if the employee is absent today, there is a 54% chance that she will be absent tomorrow. Suppose that today there are 899 employees at work. Required:
a. Find the transition matrix for this scenario.
b. Predict the number that will be at work five days from now.
c. Find the steady-state vector.