LeBow Cafeteria has four windows: salad, sandwich, dessert, and drink. Each customer spends on average 5 min, 3min, 1min and 1min at each window. There are 2, 4, 1, and 1 people serving at each window, respectively. Arriving customers first visit the salad bar and sandwich window, and among them only 80% visit dessert window, while the other 20% leave the cafeteria after buying sandwich. Only 50% of all customers visit drink window, while the others leave after buying dessert.

a. Where is the bottleneck?

b. What is the capacity of the cafeteria?

For 100 consecutive days, a company making nutritional supplements has measured the amount of a protein the company puts into its protein bars. Each day, the company takes a sample of 6 protein bars. The average across all 600 bars was 31.232 grams. The standard deviation was 0.83291 gram. In order to construct an X-bar chart, find out the center line, the upper control limit, and the lower control limit.

Camile owns Crunch Code, a company that provides quick programming solutions. Clients send Crunch projects via its web page and Crunch bangs out the needed code as quickly as possible. Camile has five programmers who do all of the coding. On average, a project arrives once every 4.8 hours, with a standard deviation of 6.00 hours. Each project is assigned to one programmer and that programmer takes, on average, 19.2 hours to complete each project, with a standard deviation of 19.2 hours.

How many uncompleted projects are waiting for a programmer, on average, at any given time?