Jawaharlal Nehru Technological University Hyderabad 2006 B.E Computer Science IV / I CSE SET3 REG[ MATHEMATICAL MODELLING AND SIMULATION ] - Question Paper

Code No: RR410508 Set No. 3
IV B.Tech I Semester Regular Examinations, November 2006
MATHEMATICAL MODELLING & SIMULATION
( Common to Computer Science & Engineering and Electronics & Computer Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
? ? ? ? ?
1. (a) discuss the term ’Artificial variable’ and its use in Linear programming. [Marks4]
(b) Solve the subsequent L. P. issue by 2 - phase method: [Marks12]
Maximize z =5x1 - 2x2 + 3x3
subject to the constraints
2x1 + 2x2 - 3x = 2
3x1 - 4x2 = 3
2x + 3x3 = 5
and x1, x2, x2 = 0.
2. A company manufacturing air - coolers has 2 plants located at Mumbai and Kolkata with capacities of 200 Units and 100 units per week respectively. The company supplies the air coolers to its 4 show rooms situated at Ranchi, Delhi, Lucknow and Kanpur which have a maximum demand of 75, 100, 100 and 30 units respectively. Due to the difference in raw material cost and transportation cost, the profit per unit in rupees differs which is shown in the table below: [Marks16]
Ranchi Delhi Lucknow Kanpur
Mumbai 90 90 100 100
Kolkata 50 70 130 85
lan the production programme so as to maximize the profit. The company may have its production capacity at any plant partly unused.
3. elaborate the costs associated with inventory? Distinguish ranging from deterministic and stochastic models in inventory theory. [Marks 16]
4. (a) State different kinds of items in inventory control techniques. [Marks 6]
(b) The subsequent thirty numbers represent the annual value in thousand of rupees of a few thirty items of materials opted at random. Carry out an ABC analysis and list out the values of ‘A’ items only: [Marks10]
1 2 4 9 75 4 25
3 6 13 2 four 12 30
100 2 7 40 15 55 1
11 15 8 19 1 20 1
3 5
5. Repairing a certain kind of machine which breaks down in a provided factory consists of five basic steps that must be performed sequentially. The time taken to perform every of the five steps is
obtained to have an exponential distribution with mean five minutes and is independent of other steps. If these machines breakdown in Poisson fashion at an avg. rate of 2 per hour and if there is only 1 repairman, what is the avg. idle time for every machine that has broken down? [Marks16]

6. (a) explain in brief [Marks 8]
i. Dummy activity
ii. Free float
iii. Independent float
iv. Total float
(b) elaborate the 3 estimates needed for PERT analysis? How do you use these estimates to calculate the expected activity time and the variance in activity time? [Marks 8]
7. List and explain different periods in the history of simulation software. [Marks 16]
8. What parameters do you consider to compare 2 system designs. Illustrate.( such as in a queuing system, perhaps 2 possible queue disciplines or 2 possible sets of servers etc.)
[Marks 16]
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Earning:   Approval pending.