A company employs four classes of machine operators (A, B, C and D); all new
employees are hired as class D and, 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 percent of class B
and 5 percent of class A employees are also separated. For each employee lost,
the company hires a new class D employee.
Required:
(i) The transition matrix. (7 marks)
(ii) The number of employees in each class two years after the agreement
with the union. (7
marks)