What is the average number of customers in the barbershop

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Reference no: EM133650249

Question 1. Favors Distribution Company purchases small, imported trinkets in bulk, packages them, and sells them to retail stores. They are conducting an inventory control study of all their items. The following data for the year 2006 are for one such item, which is not seasonal.


Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug
Sales	11	19	17	14	15	16	20	15

A. Use trend projection to estimate the relationship between time and sales (state the trend line equation in this problem).

B. Calculate forecasts for March 2007, April 2007, and January 2008

Question 2. (a) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of 12 vehicles per hour (approximately Poisson in nature). The mechanic crew can service an average of 4 vehicles every 10 minutes with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $50 per hour. The cost associated with lost productivity from the breakdown is estimated at $80 per vehicle per hour (or any fraction thereof). Which is cheaper, the existing system with one service crew, or a revised system with two service crews? The average waiting time for adding the second crew is 0.02.

(b) Peter's International Barbershop is a popular haircutting and styling saloon near the campus of the Brooklyn College. One barber is available to work full time and spend an average of 6 minutes on each customer. Customers arrive all day long at an average rate of 10 minutes Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. Explain your results.

(a) What is the probability that the shop is empty?

(b) What is the average number of customers in the barbershop?

(d) What percentage of time the barber is busy?

(e) What is the average number of customers waiting to be served?

Reference no: EM133650249

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