The Acme Manufacturing Company employs 500 machine operators. These operators are classified as apprentice, machinist, and master machinist. Company policy dictates that all new operators be hired at the apprentice level. Currently, there are 200 apprentices, 250 machinists, and 50 master machinists. Acme’s union contract specifies that of the employees that start the new year at the company, 15% in each class are to be promoted each year. It is estimated that an additional 15% of the employees that started as apprentices leave the company each year, 10% of the machinists leave, and 5% of the master machinists leave. Due to current economic conditions, the company does not rehire and replace these.

Define a Markov chain to model this situation, and construct its one-step transition matrix.