T shirts are manufactured at a factory

To produce shirts, there must be cutting and folding, which requires 1 minute on average per shirt. Three separate machines are available for this task. After the cloth is cut, a 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 of cutting/folding, printing, and inspection stations

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

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?

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