Depending on demand, a conveyor belt operates at 3 different speed levels 1,2 , and 3. A transition from level \(i\) to level \(j\) is made with probability \(p_{i j}\) with

\[p_{12}=0.8, p_{13}=0.2, p_{21}=p_{23}=0.5, p_{31}=0.4, p_{32}=0.6\]

The respective mean times the conveyor belt operates at levels 1,2 , or 3 between transitions are

\[\mu_{1}=45, \mu_{2}=30, \text { and } \mu_{3}=12 \text { [hours]. }\]

Determine the stationary percentages of time in which the conveyor belt operates at levels 1,2 , and 3 by modeling the situation as a semi-Markov chain.