During the dinner hour, the distribution of the inter-arrival time of customers at Burger Barn is predictable to be as follows:
|
Inter-arrival Time
|
Probability
|
|
30 seconds
|
.45
|
|
60 seconds
|
.25
|
|
90 seconds
|
.15
|
|
120 seconds
|
.10
|
|
150 seconds
|
.05
|
Sixty percent of customers pay along with cash, while 40% pay along with credit cards.
|
Payment Method
|
Probability
|
|
Cash
|
.60
|
|
Credit
|
.40
|
The service time of the cash and credit card customers are predictable to be as follows:
|
Cash
|
Credit Card
|
|
Service Time
|
Probability
|
Service Time
|
Probability
|
|
20 seconds
|
.35
|
30 seconds
|
.20
|
|
40 seconds
|
.30
|
60 seconds
|
.45
|
|
60 seconds
|
.25
|
90 seconds
|
.25
|
|
80 seconds
|
.10
|
120 seconds
|
.10
|
Simulate this system for 20 customer arrivals and determine the average time a cash and credit card customer must wait in line before paying the cashier. Use the random numbers in the table below to determine the customer inter-arrival time, whether the customer pays with cash or credit, the service time.
You will be working with three probabilistic variables, the inter-arrival time, the payment method and the service time. Please also use the excel template attached when solving this problem.
|
Random Numbers
|
|
Inter-arrival Time
|
Payment Method
|
Service Time
|
|
63
|
10
|
19
|
|
46
|
73
|
79
|
|
86
|
28
|
35
|
|
0
|
51
|
63
|
|
56
|
91
|
54
|
|
67
|
14
|
51
|
|
59
|
64
|
93
|
|
28
|
24
|
69
|
|
79
|
70
|
14
|
|
64
|
84
|
35
|
|
33
|
73
|
1
|
|
81
|
17
|
9
|
|
17
|
48
|
70
|
|
63
|
11
|
50
|
|
66
|
88
|
40
|
|
27
|
94
|
41
|
|
4
|
29
|
71
|
|
34
|
83
|
68
|
|
7
|
71
|
50
|
|
69
|
27
|
82
|