Problem 5. (19 points) ABC Corp. is evaluating the process at Internal Services Office that handles requests of its summer interns. Interns arrive at the Internal Services Office at an average of one every 15 minutes. The standard deviation of their inter-arrival time is 15 minutes. Only one clerk, Kristen, who works eight hours per day, staffs the service counter. On average, Kristen processes an intern’s request in 12 minutes with a standard deviation of 6 minutes.
ABC Corp. estimates that it loses $10 per hour when an intern is at the service center not working. To reduce the time an intern spends at the service center, the following two options are considered:
a)Hire a second clerk, who will work at the same rate as Kristen.
b)Replace Kristen with a senior clerk, who processes a request in 6 minutes with astandard deviation of 3 minutes.
Answer the following questions. Keep two digits after the decimal point throughout your calculation. Show your work to receive full credits.
1.(6 points) On average, how long does an intern have to wait to submit a servicerequest under options a) and b), respectively?
2.(6 points) On average, how many interns are at the service center under options a)and b), respectively?
3.(7 points) Kristen and the second clerk’s wage rates are both $10 per hour and thesenior clerk’s wage rate is $20 per hour. What are the total cost of options a) andb), respectively? Which option would you recommend based on cost savings?
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