Question 1:
United Dairies Inc., supplies milk to numerous independent grocers throughout Florida. Management wants to develop a forecast of number of half-gallons of milk sold per week. Sales data (in units) for the past twelve weeks are as follows:
|
Week
|
Sales
|
Week
|
Sales
|
|
1
|
2750
|
7
|
3300
|
|
2
|
3100
|
8
|
3100
|
|
3
|
3250
|
9
|
2950
|
|
4
|
2800
|
10
|
3000
|
|
5
|
2900
|
11
|
3200
|
|
6
|
3050
|
12
|
3150
|
Use exponential smoothing, with, 4. 0 = α to develop a forecast of demand for week 13.
Question 2:
Suppose that at a bank teller window the customers arrive in their cars at the average rate of 20 per hour according to a Poisson distribution. Suppose also that the bank teller spends an average of two minutes per customer to complete the service, and the service time is exponentially distributed. Customers, who appear from an infinite population, are served on a first-come-first-served basis, and there is no limit to possible queue length.
(i) What is the expected waiting time in system per customer?
(ii) What is the mean number of customers waiting in system?
(iii) What is the probability of zero customers in system?
(iv) What value is utilisation factor?