1. Drive Thru Coffee sells 8 oz. cups of coffee to go from a drive thru window. Past records indicate that the time between customers arriving between 8 AM and 9 AM is given in the table below

Time between customer arrivals (10 seconds) / Cumulative Probability
1 / .014
2 / .142
3 / .490
4 / .816
5 / .959
6 / .995
7 / 1.000

Records indicate that the time to place an order and get a cup of coffee is given in the table below

Service time(10 seconds) / Cumulative Probability
1 / .118
2 / .490
3 / .860
4 / .981
5 / 1.000

Assuming that arrivals and service will continue with the above patterns, use the random numbers given in the table below to simulate the first five orders of the day. Assume that the first order arrives after 8:00 AM

Customer / Random
number / Time between arrivals / Arrival time / Random number / Service time / Time server becomes free / Waiting time / Idle time
1 / .452 / 3 / 08:03 / .668 / 3 / 08:00 / 0 / 3
2 / .106 / 2 / 08:05 / .803 / 3 / 08:06 / 1 / 0
3 / .588 / 4 / 08:09 / .608 / 3 / 08:09 / 0 / 0
4 / .359 / 3 / 08:12 / .249 / 2 / 08:12 / 0 / 0
5 / .755 / 4 / 08:16 / 08:14 / 0 / 2

2. Tia Thompson owns and operates one of the largest Mercedes-Benz auto dealerships in Washington, DC. In the past 36 months, her sales have ranged from a low of 6 new cars to a high of 12 new cars, as reflected in the following table:

Sales of New Cars/Month / Frequency / Probabilty / Cumulative
6 / 3 / .083 / .083
7 / 4 / .111 / .194
8 / 6 / .167 / .361
9 / 12 / .333 / .694
10 / 9 / .250 / .944
11 / 1 / .028 / .972
12 / 1 / .028 / 1.000
36 / 1

Thompson believes that sales will continue during the next 24 months at about the same historical rates, and that delivery times will also continue to follow the following pace(stated in probability form):

Delivery Time (in months) / Probability / Cumulative
1 / .44 / .44
2 / .33 / .77
3 / .16 / .93
4 / .07 / 1.000
1

Thompson’s current policy is to order 14 cars at a time (2 full truckloads, with 7 autos on each truck), and to place a new order whenever the stock on hand reaches 12 autos. What are the results of this policy when simulated over the next

2 years?

MonthBeginning Inventory r nSalesEnding Inventory r nLead Time Stock Out

1 14 .47 95.61 2 0

2 5 .69 90.29 4

3 0 .55 9 0.48 9

4 14 .82 104.91 3 0

5 4 .71 100.42 6

6 0 .22 80.54 8

7 0 .93 100.23 10

8 14 .35 86.73 2 0

9 6 .64 90.46 3

10 0 .02 60.20 6

11 14 .43 95.34 1 0

12 5 .59 90.59 4