a. What is the average number of patients you would expect to see in Dr. Martin's facilities? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number of patients b. How long would it take for a patient to arrive, get an injection, and leave? (Round your answer to 2 decimal places.) Average total time ]minutes c. What is the probability that there will be three or more patients on the premises? (Do not round intermediate calculations. Round your answer to 1 decimal place.) Prohability
a. What is the average number of patients you would expect to see in Dr. Martin's facilities? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number of patients b. How long would it take for a patient to arrive, get an injection, and leave? (Round your answer to 2 decimal places.) Average total time ]minutes c. What is the probability that there will be three or more patients on the premises? (Do not round intermediate calculations. Round your answer to 1 decimal place.) Prohability
Practical Management Science
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Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Question
Transcribed Image Text:exhibit 7.12
Expected Number of People Waiting in Line (L) for Various Values of S and A/u
NUMBER OF SERVICE CHANNELS, S
A/u 1
2
3
4
5
6
7
8
9
10
11
12
13 14
15
0.10
015
0.20 0.0500 0.0020
0.25 0.0833 0.0039
0.30 01285 0.0069
0.35 0.1884 0.010
040 02666 0.0166
045 0.3681 0.0239 0.0019
0.50 0.5000 0.0333 0.0030
0.55 0.6722 0.045 0.0043
0.60 0.9090 0.0593 0.0061
0.65
0.70
0.75
0.80
0.85
0.90
0.95 18.0500 02767 0.0371 0.0053
0.0264 0.0006
Employee
nt
Shannon Mcirth
Meli nta Dvem
Excel:
1.2071 0.0767 0.0084
1.6333 0.0976 0.012
2.2500 0.1227 0.0147
3.2000 0.1523 0.0189
4.8165 0.1873 0.0239 0.0031
8.1000 02285 0.0300 0.0041
Еxpected
Length
1.0
1.2
1.4
1.6
1.8
0.3333 0.0454 0.0067
0.6748 0.0940 0.0158
1.3449 O1778
2.8441
7.6731
0.0324 0.0059
0.0604 0.0121
0.0227
0.3128
0.5320 0.1051
0.0047
08888 O1730
14907
2.1261
4.9322
12.2724
0.0390 0.0090
2.0
2.2
24
2.6
2.8
0.2770 0.066
04205 0.1047
0.6581 0.1609 0.0425
0.241
0.0158
0.0266
0.0065
0.0110
0.0659 0.0180
1.0000
3.0
3.2
3.4
3.6
3.8
1.5282 0.3541 0.0991 0.0282 0.0077
2.3855 0.5128 01452 0.0427 0.0122
3.9060 07365 02085 0.0631 0.0189
7.0893 1.0550 02947 0.0912 0.0283
16.9366 1.5181
0.0084
0.0127
04114
0.1292 0.0412
4.0
4.2
4.4
4.6
4.8
22164
3.3269 07837
52675 1.0777 0.3364 0.142
9.2885 14857
21.6384 2.0708
0.0189
0.0273
0.0389
0.0541
0.0742
05694 0.1801
0.0590
0.2475 0.0827
0.0087
0.0128
0.4532 0.1555
0.6071 0.2092
0.0184
0.0260
0.1006
0.0361
5.0
5.2
5.4
5.6
5.8
2.9375
4.3004
6.6609
11.5178
26.3726 2.6481
0.8102 0.2785
0.0125
0.0492 0.0175
0.0663 0.0243 0.0085
0.0683 0.0330 0.019
0.164 0.0443 0.0164
1.0804
1.4441
0.3680 0.1345
0.5871
1.9436 0.6313
0.8225
0.1779
0.2330
0.3032
6.0
6.2
6.4
6.6
6.8
3.6878 1.0707
5.2979 1.3967
8.0768 1.8040
13.7992 24198
31.1270
0.3918
0.5037
0.6454
0.8247
1.0533
0.1518 0.0590 0.0224
0.1964 0.0775 0.0300 0.0113
0.2524 0.1008 0.0398 0.0153
03222 0.1302 0.0523 0.0205
04090 0.1666 0.0679 0.0271 0.0105
32441
7.0
7.2
7.4
7.6
7.8
44471
6.3133
9.5102
16.0379
35.8956
13471
17288
2.2324
2.9113
3.8558
0.5172 0.2119 0.0676 0.0357 0.0141
0.6521 0.2677 0.19 0.0463 0.0187
0.8202 0.3364 0.1420 0.0595 0.0245 0.0097
10310
1.2972
04211 O.789 0.0761 0.0318 0.0129
0.5250 0.2243 0.0966 0.0410 0.0168
8.0
8.2
8.4
8.6
8.8
5.2264
7.3441
10.9592
18.3223
40.6824
16364
2.0736 0.8109 0.3469 0.1520 0.0663 0.0283
2.6470 1.0060 0.4288 0.1891 0.0834 0.0361
3.4160
4.4805 1.5524 0.6501 0.2885 0.1208 0.0577
0.6530 02796 01214 0.0522 0.0220
1.2484 0.5236 0.2341 0.1043 0.0459
9.0
9.2
9.4
9.6
9.8
6.0183 19366 07980 03543 0.1603 0.0723
8.3869 24293 0.9788 04333 0.1974 0.0899
12.4183
20.6160 3.9318 14752 0.5437 02952 0.1367
45.4769 5.1156
3.0732 1.2010 0.5267 02419 0.111
1.8165
0.7827 0.3699 0.16731
10
6.8210
2.2465 0.9506 04352 0.2040
w wW w wN~ NNN
Transcribed Image Text:L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients
arrive for an injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two
nurses. The specific injections for a patient are prepared, and the patient is called through a speaker system into the room to receive
the injection. At certain times during the day, patient load drops and only one nurse is needed to administer the injections. Use Exhibit
712.
Let's focus on the simpler case of the two-namely, when there is one nurse. Also, assume that patients arrive in a Poisson fashion
and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an interarrival time of
approximately 3 minutes. It takes the nurse an average of 2.50 minutes to prepare the patients' serum and administer the injection.
a. What is the average number of patients you would expect to see in Dr. Martin's facilities? (Do not round intermediate calculations.
Round your answer to 2 decimal places.)
Average number of patients
b. How long would it take for a patient to arrive, get an injection, and leave? (Round your answer to 2 decimal places.)
Average total time
|minutes
c. What is the probability that there will be three or more patients on the premises? (Do not round intermediate calculations. Round
your answer to 1 decimal place.)
Probability
%
d. What is the utilization of the nurse? (Do not round intermediate calculations. Round your answer to 1 decimal place.)
Utilization of the nurse
e. Assume three nurses are available. Each takes an average of 3.00 minutes to prepare the patients' serum and administer the
injection. What is the average total time of a patient in the system? (Do not round intermediate calculations. Round your answer to 2
decimal places. Do not interpolate your /u ratio when using Exhibit 7.12. Use the closest Nµ ratio appearing in the table.)
Average total time
|minutes
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