A HS football jerseys are in high demand. The process of manufacturing the jerseys is as follows. • To produce the jerseys, raw material is first cut into cloths for individual jerseys. This step requires 1 minute on average for each jersey and there are three separate machines available for this task. • After the cloth is cut, the player number and last name are printed on the jerseys. There are three printing machines, each of which can print on one jersey in 45 seconds. • The printed jersey is then reviewed and packaged by a quality control worker. On average, this takes 90 seconds per jersey, but the standard deviation of this inspection step is 2 minutes. There are five quality control employees for this task. • Orders for jerseys arrive at exponentially distributed intervals, with an average of 160 orders per hour. • From beginning to end, the average time to produce one jersey is 4.5 minutes. • The 1a question has been solved - The capacity A, cut the cloth is 180 jerseys per hour; Capacity B, printing jersey is 240 jerseys per hour, and the Capacity C, packaging and quality control is 200 jerseys per hour. • The 1b question has also been resolved – on average, there are 8/3 = 2.6667 jerseys at the cutting step and 7.21 jerseys at the inspection step, and 2.12 jerseys in the printing step. • The question 1c has also been resolved - to reduce average wait time, the factory wants to reduce the utilization of the inspection workers to 4/7 = 57.14%. thus total 7 workers should there be at the inspection step in order to achieve this. Now question 1d, Under the new staffing derived in 1c, what is the new average waiting time (in minutes) at the inspection step? The correct answer provided is 0.13 minutes. Please help to calculate and explain it.
I tried to use Little’s Law, L = λW, but I cannot get to the right answer.