Assignment 1

1. A company employs four classes of machine operators (A, B, C and D), all new employees are hired as class D, through a system of promotion, may work up to a higher class. Currently, there are 200 class D, 150 class C, 90 class B and 60 class A employees. The company has signed an agreement with the union specifying that 20 percent of all employees in each class be promoted, one class in each year. Statistics show that each year 25 percent of the class D employees are separated from the company by reasons such as retirement, resignation and death. Similarly, 15 percent of class C, 10 per cent of class B and 5 per cent of class A employees are also separated. For each employee lost, the company hires a new class D employee.

Required: The transition matrix and the number of employees in each class three years after the agreement with the union.