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Posted By: Sri Member Level: Gold Posted Date: 15 Nov 2007
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2007 Jawaharlal Nehru Technological University B.E Computer Science IV / I CSE SET1 [ MATHEMATICAL MODELLING AND SIMULATION ] Question paper
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Code No: RR410508 SET NO:1
IV B.Tech I Semester Supplementary Examinations, February 2007
MATHEMATICAL MODELLING &SIMULATION
(Common to Computer Science & Engineering and Electronics & Computer Engineering)
Time: 3 hours Max Marks:80
Answer any FIVE Questions
All Questions carry equal marks
*****
1. a) What are various phases of O.R.problem? Explain them Briefly?[Marks 6]
b) A toy manufacturer produces two types of dolls : a basic version doll A and a deluxe version doll B. Each doll of type B takes as long to produce as one doll of Type A. The company have time to make a maximum of 2000 dolls per day and each type requires equal amount of it. The deluxe version, i.e. type B requires a fancy dress of which there are only 600 per day available. If the Company makes a profit of Rs.30 and Rs.50 per doll, respectively on doll A and B; how many of each should be produced per day in order to maximize profit? Solve it by Graphical method. [Marks 10]
2. a) Give an algorithm to solve an “Assignment” problem? [Marks 8 ]
b) What is an unbalanced assignment problem? Explain it with at least one example. [Marks 8 ]
3.a) What is meant by inventory? Give the classification of different inventory Models [Marks 6 ]
b) ABC manufacturing company purchase 9,000 parts of a machine for its annual requirement,ordering one month’s usage at a time.Each part costs Rs.20. The ordering cost per order is Rs.15, and the carrying charges are 15% of the average inventory per year.
You have been asked to suggest a more economical purchasing policy for the company. What advice would you offer and how much would it save the company per year? [Marks 10 ]
4.a) State various types of items in inventory control techniques. [Marks 6 ]
b) The following thirty numbers represent the annual value in thousand of rupees of some thirty items of materials selected at random. Carry out ABC analysis and list out the value of ‘A’ items only: [Marks 10 ]
1 2 4 9 75 4 25
3 6 13 2 4 12 30
100 2 7 40 15 55 1
11 15 8 19 1 20 1
3 5
5.a) Consider a self service store with one cashier. Assume passion arrivals and exponential service times. Suppose that a customer arrive on the average every 5 minutes and the cashier can serve 10 in 5 minutes . Find
a) The average numbers of customers queuing for service.
b) The probability of having more than 10 customers in the system.
c) The probability that a customer has no queue for more than 2 minutes
If the service can be speeded upto 12 in 5 minutes by using a different cash register, what will be the effect on the quantities (a),(b) and(c) [Marks 16 ]
6. The following table gives the information about various activities of a project network.
Activity Normal Duration(Days) Normal Cost(Rs.) Crash Duration(Days) Crash Cost(Rs.)
1-2 9 8,000 7 10,000
1-3 5 5,000 3 8,000
2-3 7 7,000 5 8,600
2-4 8 6,000 6 7,000
3-4 6 9,000 4 11,400
The overhead costs are Rs.1,300 per day. Determine the optimum cost and duration of the Project. [Marks 16 ]
7.The execution of simulation algorithm in [Marks 8 + Marks 8 ]
a) SIMSCRIPT
b) GPSS
8.a) What is the importance of Histograms in input modeling? How do you construct a Histogram. [Marks 12 ]
b) List out various probability distributions used in input modeling.[Marks 4 ]
*****
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