Jawaharlal Nehru Technological University Hyderabad 2006 B.E Computer Science mathematical modelling and stimulation(MMS) - - Question Paper

iii. Clock time
(c) discuss the representation of time in discrete system simulation. [4]
8. explain the steps in the development of a useful model of input data with suitable
example. [16]
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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. [4]
(b) Solve the subsequent L. P. issue by 2 - phase method: [12]
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 Kanapur which have a maximum demand of 75, 100, 100 and 30 units
respectively. Due to the dierence in raw material cost and transportation cost,
the profit per unit in rupees diers which is shown in the table below: [16]
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. [16]
4. (a) State different kinds of items in inventory control techniques. [6]
(b) The subsequent thirty numbers represent the annual value in thousand of ru-
pees of a few thirty items of materials opted at random. Carry out an ABC
analysis and list out the values of ‘A’ items only: [10]
1 two four nine 75 four 25
3 six 13 two four 12 30
100 two seven 40 15 55 1
11 15 eight 19 one 20 1
3 5
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Code No: RR410508 Set No. 3
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? [16]
6. (a) explain in brief [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? [8]
7. List and explain different periods in the history of simulation software. [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.) [16]
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Code No: RR410508 Set No. 4
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) describe slack and surplus variables as involved in the L. P. P. How are these
variables useful in solving a L. P. P. [4]
(b) Solve the subsequent L. P. P. by simplex method : [12]
Maximize z = 4x1 + x2 + 4x3 + 5x4
subject to the constraints
4x1 + 6x2 - 5x3 + 4x4  -20
3x1 - 2x2 + 4x3 + x4  10
8x1 - 3x2 - 3x3 + 2x4  20
and x1, x2, x3, x4  0.
2. (a) describe constrained optimization issue in non - linear programming prob-
lem? [8]
(b) Write a short note on Kuhn - Tucker condition [8]
3. (a) discuss the decision rules for a purchase inventory model with 2 price breaks
[4]
(b) obtain the optimal order volume for a product for which the price breaks are
as follows: [12]
volume Unit cost(Rs.)
0  q1 < 50 Rs.10
50 < q2 < 100 Rs.9
100 < q3 Rs.8
The monthly demand for the product is 200 units, the cost of storage is 25%
of the unit cost and ordering cost is Rs. 20 per order.
4. What is the ABC analysis? Why it is necessary? elaborate the basis steps in
implementary it? [16]
5. A telephone exchange has 2 long distance operators. The telephone company
obtains that, during the peak load, long distance calls arrive in a poisson fashion at a
an avg. rate of 15 per hour. The length of service on these calls is approximately
exponentially distributed with mean length of five minutes. [16]
(a) What is the probability that a subscriber will have to wait for his long distance
call during the peak hours of the day.
(b) If the subscriber will wait and serviced in turn, what is the expected waiting
time? Establish the formula used.
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Code No: RR410508 Set No. 4
6. (a) discuss PERT and its importance in network analysis. elaborate the require-
ments for applications of PERT techniques. [10]
(b) List at the dierences ranging from PERT and CPM [6]
7. (a) discuss the role of state descriptor in discrete system simulation [6]
(b) describe the terms [6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) discuss the representation of time in discrete system simulation. [4]
8. (a) What is the importance of Histograms in input modeling? How do you con-
struct a Histogram. [12]
(b) List out different probability distributions used in input modeling. [4]
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Earning:   Approval pending.