Thesoccer team shirtsare manufactured at a factory in Hongkong. To produce shirts, the cloth must first be cut and folded, which requires 1 minute on average for each shirt. Three separate machines are available for this task. After the cloth is cut, the team logo is printed on the shirts. There are three printing machines, each of which can print on one shirt in 45 seconds.

Finally, the printed shirt is then reviewed and packaged by a quality control worker. On average, this takes 90 seconds per shirt, but the standard deviation of this inspection step is 2 minutes. There are five quality control employees for this task. Orders for shirts arrive at exponentially distributed intervals, with an average of 160 orders per hour.

From beginning to end, the average time to produce one shirt is 4.5 minutes.

1. Find the capacity at each resource.

Answer:

Capacity A =180 shirts per hour

Capacity B = 240 shirts per hour

Capacity C = 200 shirts per hour

2. On average, there are 8/3=2.667shirts at the cutting step and 7.21 shirts at the inspection step. How many items are on average in the printing step?

Answer: 2.1233 items

3. To reduce average wait time, the factory wants to reduce the utilization of the inspection workers to 4/7 = 57.14%. How many total workers should there be at the inspection step in order to achieve this?

Answer : 7 workers

4. Under the new staffing derived in(3), what is the new average waiting time (in minutes) at the inspection step?

Answer: 0.1296 min

I need step by step explanation of the given answers.