A computer help desk receives new daily customer arrivals(Answered)
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Question
 A computer help desk receives new daily customer arrivals according to the following probability distribution:
# Arrivals  Probability  Random # 
0  0.05  0105 
1  0.2  0625 
2  0.3  2655 
3  0.2  5675 
4  0.15  7690 
5  0.1  9100 
The number of customers that the help desk has the capability to serve per day is based on the following probability distribution:
# Served  Probability  Random # 
3  0.5  0150 
4  0.3  5180 
5  0.2  8100 
If the number of arrivals exceeds the # served capability, the customers will receive top priority the next day. The random numbers drawn for a 5day simulation are as follows:
Arrival Random #  Service random # 
19  95 
34  95 
39  92 
90  33 
97  85 
What will the average number of delays be for the 5day simulation?
0.9/day  
1.2/day 
None of the alternatives are correct.  
0.4/day 
2.1/day 
Demand per day 
0 
1 
2 
3 
4  Lead Time 
1 
2 
Probability  0.15  0.2  0.3  0.2  0.15 
 0.80  0.20 
Random #  0115  1635  3665  6685  8600 
 0180  8100 
The store orders 4 refrigerators per day to have in stock to meet demand. They are trying to maintain low inventory levels. The holding cost is $5/unit/day. The ordering cost is $20 per order. The lost sale cost is $10/unit. A simulation is to be developed to estimate the average daily inventory cost over 5 days. The table below shows the random numbers to be used for refrigerator demand and lead time on orders:
 demand random number  lead time random number 
day 1  88  54 
day 2  27  94 
day 3  32  44 
day 4  36  75 
day 5  54  71 
Assuming that beginning inventory is equal to 5 with no prior orders in transit, what is the overall average daily cost of inventory for the 5 days?
$32.  
$53 
24  
None of the alternatives are correct. 
$45 
 A certain grocery store has noted the following figures with regard to the number of people who arrive at its three checkout stands ready to check out, and the time it takes to check out the individuals.
Arrivals/Min.  Frequency  Service Time in Min  Frequency 
0  0.3  1  0.1 
1  0.5  2  0.3 
2  0.2  3  0.4 

 4  0.2 
Create an appropriate table of interval of random numbers for both variables.
Answer:
Arrivals  Interval of Random #s  Service Time  Interval of Random #s 
0  0130  1  0110 
1  3180  2  1140 
2  8100  3  4180 

 4  8100 
The time between arrivals at a drivethrough window of a fastfood restaurant follows the distribution given below. The service time distribution is also given in the table below. Use the random numbers provided to simulate the activity of the first five arrivals. Assume that the window opens at 11:00 a.m. and the first arrival after this is based on the first interarrival time generated.
Time Between Arrivals  Probability  Service Time  Probability 
1  0.2  1  0.3 
2  0.3  2  0.5 
3  0.3  3  0.2 
4  0.2 


Random numbers for arrivals: 14, 74, 27, 03
Random numbers for service times: 88, 32, 36, 24
What times does the fourth customer leave the system?
11:06.  
None of the alternatives are correct. 
11:09  
11:04. 
11:08. 
 The table below represents the probability distribution for machine breakdowns in a day of operation.
Number of breakdowns  Probability  Interval of Random Numbers 
0  0.20  120 
1  0.30  2150 
2  0.35  5185 
3  0.15  8600 
According to the table, if a random number of 00 is drawn, what would the simulated number of breakdowns be?
Not enough information provided  
2 
0  
3 
1 
 The table below represents the probability distribution for machine breakdowns in a day of operation.
Number of breakdowns  Probability  Interval of Random Numbers 
0  0.20  120 
1  0.30  2150 
2  0.35  5185 
3  0.15  8600 
According to the table, what is the probability of at least one breakdown?
0.5  
0.8 
0.3  
0.2 
0.85 
1. A computer help desk receives new daily customer arrivals according to the following
probability distribution:
# Arrivals Probability
0
0.05
1
0.2
2
0.3
3
0.2
4
0.15
5
0.1
Random #
0105
0625
2655
5675
7690
9100
The number of customers that the help desk has the capability to serve per day is based on the
following probability distribution:
# Served
3
4
5
Probability
0.5
0.3
0.2
Random #
0150
5180
8100
If the number of arrivals exceeds the # served capability, the customers will receive top priority
the next day. The random numbers drawn for a 5day simulation are as follows:
Arrival
Random #
19
34
39
90
97
Service
random #
95
95
92
33
85
What will the average number of delays be for the 5day simulation?
0.9/day
1.2/day
None of the alternatives are correct.
0.4/day
2.1/day
2. The demand for refrigerators at an appliance store adheres to the following probability
distribution:
Demand per
day
Probability
Random #
Lead
0
1
2
3
4
Time 1
2
0.15 0.2
0.3
0.2
0.15
0.80 0.20
0115 1635 3665 6685 8600
0180 8100
The store orders 4 refrigerators per day to have in stock to meet demand. They are trying to
maintain low inventory levels. The holding cost is $5/unit/day. The ordering cost is $20 per
order. The lost sale cost is $10/unit. A simulation is to be developed to estimate the average daily
inventory cost over 5 days. The table below shows the random numbers to be used for
refrigerator demand and lead time on orders:
day
day
day
day
day
1
2
3
4
5
deman
d
rando
m
numbe
r
88
27
32
36
54
lead
time
rando
m
numbe
r
54
94
44
75
71
Assuming that beginning inventory is equal to 5 with no prior orders in transit, what is the
overall average daily cost of inventory for the 5 days?
$32.
$53
24
None of the alternatives are correct.
$45
3. A certain grocery store has noted the following figures with regard to the number of people
who arrive at its three checkout stands ready to check out, and the time it takes to check out
the individuals.
Arrivals/Mi
n.
0
1
2
Frequency
0.3
0.5
0.2
Service Time
Frequency
in Min
1
0.1
2
0.3
3
0.4
4
0.2
Create an appropriate table of interval of random numbers for both variables.
Answer:
Arrivals
0
1
2
Interval of
Random
#s
0130
3180
8100
Service Time
Interval of
Random #s
1
2
3
4
0110
1140
4180
8100
The time between arrivals at a drivethrough window of a fastfood restaurant follows the
distribution given below. The service time distribution is also given in the table below. Use the
random numbers provided to simulate the activity of the first five arrivals. Assume that the
window opens at 11:00 a.m. and the first arrival after this is based on the first interarrival time
generated.
Time
Between
Arrivals
1
2
3
4
Probability Service Time Probability
0.2
0.3
0.3
0.2
1
2
3
0.3
0.5
0.2
Random numbers for arrivals: 14, 74, 27, 03
Random numbers for service times: 88, 32, 36, 24
What times does the fourth customer leave the system?
11:06.
None of the alternatives are correct.
11:09
11:04.
11:08.
4. The table below represents the probability distribution for machine breakdowns in a day of
operation.
Number of
breakdowns
0
1
2
3
Probability
0.20
0.30
0.35
0.15
Interval of
Random Numbers
120
2150
5185
8600
According to the table, if a random number of 00 is drawn, what would the simulated number of
breakdowns be?
Not enough information provided
2
0
3
1
5. The table below represents the probability distribution for machine breakdowns in a day of
operation.
Number of
breakdowns
0
1
Probability
0.20
0.30
Interval of
Random Numbers
120
2150
2
3
0.35
0.15
5185
8600
According to the table, what is the probability of at least one breakdown?
0.5
0.8
0.3
0.2
0.85
Paper#9209176  Written in 27Jul2016
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