IT TECHNICIAN
SIMULATION AND MODELING QUIZ
1. Dr Strong is a dentist who schedules all her patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending upon the type of dental work to be done. The following table shows the various categories of work, their probabilities and the time actually needed to complete the work category Time required in mins
Probability
Filling
Crowning
Cleaning
Extraction
Checkup
45
60
15
45
15
0.25
0.15
0.25
0.10
0.25 Simulate the dentist’s clinic for about four hours and determine the average waiting time for the patients and the percentage idle time for the dentist. Assume that all the patients show up at the clinic at exactly their scheduled arrival time starting at 8.00AM. Use the following random numbers 40, 82,11,34,52,66,17,and 70
2. Generate 20 random numbers and solve the following integrals by monte-carlo
(i) (ii)
3. A piece of equipment contains four identical tubes and can function only if all the four are in working order. The lives of tubes has approximately uniform distribution from 1000 to 2000 hours. The current maintenance practice is to replace a tube when it fails. Equipments has to be shut down for 1 hr for replacing a tube, the cost of one tube is sh 100, while the shut down time cost sh 200 per hour. Simulate the system for about 6000 hrs of run and find the maintenance cost using the following random numbers 0.8,0.2,0.6,0.3,0.1,0,0.8,0.9,0.2,0.8,0.3,0.7,0.4,0.8,0.5,0.6,0,0.4,0.9
4. A newsstand can buy a daily newspaper for sh 50 each and sell it for sh 85. The unsold copies if any can be disposed off as waste paper at sh 20 each. The estimated daily demand distribution is as follows
Demand (no of copies) 100 110 120 130 140 150 160 170 180
Probability 0.03 0.07 0.19 0.28 0.20 0.10 0.05 0.05 0.03
Generate uniformly distributed random numbers and determine the optimal number of newspaper copies which should be procured, so that
1. Dr Strong is a dentist who schedules all her patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending upon the type of dental work to be done. The following table shows the various categories of work, their probabilities and the time actually needed to complete the work category Time required in mins
Probability
Filling
Crowning
Cleaning
Extraction
Checkup
45
60
15
45
15
0.25
0.15
0.25
0.10
0.25 Simulate the dentist’s clinic for about four hours and determine the average waiting time for the patients and the percentage idle time for the dentist. Assume that all the patients show up at the clinic at exactly their scheduled arrival time starting at 8.00AM. Use the following random numbers 40, 82,11,34,52,66,17,and 70
2. Generate 20 random numbers and solve the following integrals by monte-carlo
(i) (ii)
3. A piece of equipment contains four identical tubes and can function only if all the four are in working order. The lives of tubes has approximately uniform distribution from 1000 to 2000 hours. The current maintenance practice is to replace a tube when it fails. Equipments has to be shut down for 1 hr for replacing a tube, the cost of one tube is sh 100, while the shut down time cost sh 200 per hour. Simulate the system for about 6000 hrs of run and find the maintenance cost using the following random numbers 0.8,0.2,0.6,0.3,0.1,0,0.8,0.9,0.2,0.8,0.3,0.7,0.4,0.8,0.5,0.6,0,0.4,0.9
4. A newsstand can buy a daily newspaper for sh 50 each and sell it for sh 85. The unsold copies if any can be disposed off as waste paper at sh 20 each. The estimated daily demand distribution is as follows
Demand (no of copies) 100 110 120 130 140 150 160 170 180
Probability 0.03 0.07 0.19 0.28 0.20 0.10 0.05 0.05 0.03
Generate uniformly distributed random numbers and determine the optimal number of newspaper copies which should be procured, so that