Please do the following questions in separate excel sheets using excel solver please:
1. The reference desk at a library receives requests for assistance. Assume that a Poisson
probability distribution with a mean rate of 10 requests per hour can be used to describe the
arrival pattern and that service times follow the exponential probability distribution with a mean
service rate of 12 requests per hour.
a. What is the probability of no requests for assistance in the system?
b. What is the average number of requests that will be waiting for service?
c. What is the average waiting time in minutes before service begins?
d. What is the average time at the reference desk in minutes (waiting time plus service time)?
e. What is the probability that a new arrival has to wait for service?
2. ABC Design provides decorating assistance to its customers. In normal operations, an average
of 2.5 customers arrive each hour. One design consultant is available to answer questions and
make product recommendation. The consultant averages 10 minutes with each customer.
a. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and
exponential service times.
b. Service goals dictate that an arriving customer should not wait for service more than an average of 5
minutes. Is this goal being met? If not, what action do you recommend?
c. If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean
service rate? Will the service goal be met?
3. Mike’s television repair service receives an average of six TV sets per eight-hour day to be
repaired. The service manager would like to be able to tell customers that they can expect oneday
service. What average repair time per set will the repair shop have to achieve to provide oneday
service on the average? (Assume that the arrival rate is Poisson distributed and repair times
are exponentially distributed).
4. A vending machine at a bus terminal dispenses hot coffee, hot chocolate, or hot tea, in a
constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of
60 per hour (Poisson distributed). Determine the average length of the waiting line and the
average time a customer must wait.
5. A motorcycle dealer wants to be able to accurately forecast US demand for their best-selling
motorcycle during the next month. Because the manufacturer is in Asia, it is difficult to send
motorcycles back or reorder if the proper number is not ordered a month ahead. From sales records,
the dealer has accumulated the following data for the past year.
Month Motorcycle Sales
a. Compute a three-month moving average forecast of demand for April through January (of the next
b. Compute a five-month moving average forecast for June through January.
c. Compare the two forecasts computed in parts a and b, using MAD. Which one should the dealer use
for January of the next year? Justify your answer.
6. The chairperson of the department of management at a university wants to forecast the number of
students who will enroll in production and operations management (POM) next semester in order to
determine how many sections to schedule. The chair has accumulated the following enrollment data
for the past eight semesters.
Semester Students Enrolled in POM
a. Compute a three-semester moving average forecast for semesters 4 through 9.
b. Compute the exponentially smoothed forecast (α = .20) for the enrollment data.
c. Compare the two forecasts using MAD and indicate the more accurate.
7. A mutual fund of growth stocks has had the following average monthly price for the past 10
Month Fund Price
a. Compute the exponentially smoothed forecast with α = .40.
b. Using linear trend analysis, develop a forecasting model for the fund price. What is the linear
equation that best fits the data?
c. Which of the methods analyzed here would you use? Explain your answer.
Please finish all these 7 questions in excel using solver wherever necessary and email me the excel files. Kindly do asap as I am on a harsh deadline.
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