Math 311

Class 27

“Santa’s workshop”

A charity group organizes a fundraiser in a form of workshop where participants can create their own holiday ornament. The workshop consists of several stations:

• At the first station, participants can cut one or more pieces of wood. Participants arrive at rate 18 per hour. The service rate is 25 customers per hour.
• At the second station participants glue their wood pieces together. The service rate is 30 customers per hour. Some customers bring their own pieces of wood, and come directly to this station, at the rate of 3 per hour.
• At the third station participants can carve and sand their wood pieces. The service rate is 7 customers per hour. Again, participants can bring their own wood and come directly to this station, at the rate 0.5 customers per hour.
• At the fourth and fifth station, participants apply red (fourth station) or green (fifth station) paint. Both station have service rates of 40 customers per hour, and customers come from the outside at the rate of 0.1 customer per hour.
• At the sixth station, customers apply glitter and other decorations. This station can serve up to 60 customers per hour.

Santa’s workshop cont.

• From station 1, 70% of participants proceed to station 2, 5% to station 3, 12% each to stations 4 and 5, and 1% to station 6.
• From station 2, 2% of customers proceed to station 3, 30% to station 4, 60% to station 5, and the rest to station 6.
• From station 3, 70% of participants go to station 4, 20% to station 5, and 10% to station 6.
• From station 4, 30% go to station 5, and 60% to station 6.
• From station 5, 30% go to station 4, and 60% to station 6.

\[ \begin{bmatrix} 0 & .7 & .05 & .12 & .12 & .01\\ 0 & 0 & .02 & .3 & .6 & .08\\ 0 & 0 & 0 & .7 & .2 & .1 \\ 0 & 0 & 0 & 0 & .3 & .6\\ 0 & 0 & 0 & .3 & 0 & .6\\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix} \]