Please provide math/details The Cafeteria has four windows: salad, sandwich, des

Question

Please provide math/details

The 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?

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?

Explanation / Answer

Salad window:

Sandwich window:

Dessert window:

Dessert window:

a) Maximum utilization is 0.0417 . It is of Salad window. Therefore Salad window is the bottleneck.

b) Capacity of the process is equal to , when utilization of bottleneck is 100%  

Therefore, 0.0417 = 1

or, = 1/0.0417 = 24 per hour

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