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Office Equipment Case Problem

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1. λ = 1 call/50 hours = 0.02 calls per hour

2. Mean service time = travel time + repair time = 1 + 1.5 = 2.5 hours μ = 1 / 2.5 hours = 0.4 customers per hour
3. The travel time is 1 hour. While this is considered part of the service time it actually means that the customer will be waiting during the first hour of the service time. Thus, travel time must be added to the time spent in line as predicted model in order to determine the total customer waiting time.

4. I would agree with the service guarantee since the average travel time is 1 hour for the service technician to reach the new customer's office, the total customer waiting time is 1.6082 + 1 = 2.6082 hours. Thus, the one technician is able to meet the company's 3-hour service guideline. The total cost is $155.93 per hour.

Probability that no customers are in the system 0.5380
Average number of customers waiting 0.2972
Average number of customers in the system 0.7593
Average time a customer spends in the waiting line 1.6082 hours
Average time until the machine is back in operation 4.1082 hours
Probability of a wait more than one hour 0.4620
Hours a week the technician is not on service calls (0.5380) x 40 hours =21.5 hours
Total cost per hour for the service operation $155.93
5. If the company continues to use one technician when the customer base expands to 20 customers, the average time in the waiting line will increase to 6.9454 hours. With an average travel time of 1 hour, the average total waiting time will be 6.9454 + 1 = 7.9454 hours. The total cost will be $397.78 per hour. This average total waiting time is too long and a second technician is definitely necessary.

Probability that no customers are in the system 0.3525
Average number of customers in the waiting line 0.2104
Average number of customers in the system 1.1527
Average time a

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