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7 April, 01:15

The Bijou Theater in Hermosa Beach, California, shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers' parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers don't get in until after the feature has started.) a. What is the average customer time in the system?

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  1. 7 April, 01:36
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    Task a:

    What is the average customer time in the system?

    Answer: 30 seconds

    Task b:

    What would be the effect on customer time in the system of having a second ticket taker doing nothing, but validations and card punching, thereby cutting the average service time to 20 seconds?

    Answer: 33.34 minutes

    Task c:

    Would system waiting time be less than you found in b if a second window was opened with each service doing all three tasks?

    Answer: 16.67 minutes

    Explanation:

    Task a:

    What is the average customer time in the system?

    Solution:

    Average customer time = 30 seconds per customer.

    Total number of customers in an hour = 100.

    Total time taken to attend customers = time per customer*total customers

    = 30*100 = 3,000 seconds or 50 minutes.

    So, 100 customers are attended in 50 minutes.

    Average time = 50/100 = 0.5 minutes or 30 seconds

    Task b:

    What would be the effect on customer time in the system of having a second ticket taker doing nothing, but validations and card punching, thereby cutting the average service time to 20 seconds?

    Solution:

    If the average service time is reduced to 20 seconds, the customer time will reduce in the system.

    For 100 customers, total time taken = 20*100 = 2,000 seconds or 33.34 minutes

    Thus waiting time for the 100th customer has fallen from 50 minutes to 33.34 minutes.

    Task c:

    Would system waiting time be less than you found in b if a second window was opened with each service doing all three tasks?

    Solution:

    In this case, 100 customers will be divided into 1/3rd each i. e. 100/3 in each line.

    So, waiting time for the 100/3th customer = 100/3*original time = 100/3*30 seconds = 1,000 seconds or 16.67 minutes.

    Thus, within 16.67 minutes the line would be serviced.

    Therefore, System waiting time will be less than as calculated in b.
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