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Posted By: phani Member Level: Bronze Posted Date: 11 Mar 2008
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2006 Jawaharlal Nehru Technological University B.E Computer Science mathematical modelling and stimulation(MMS) nov-2006 Question paper
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Code No: RR410508 Set No. 1
IV B.Tech I Semester Regular Examinations, November 2006
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 is a model? Discuss various classification schemes of models. [6]
(b) Find all basic solutions for the problem [10]
Max z = x1 + 2x2
such that
x1 + x2 10
2x1 - x2 40
and x1, x2 0.
2. (a) Distinguish between pure and mixed integer programming problem. [4]
(b) Find the optimal integer solution to the following all L.P. P. [12]
Maximize z =x1 + 2x2
subject to the constraints
2x2 7
x1 + x2 7
2x1 11
x1, x2 0 and x1, x2 are integers.
3. (a) Explain the relevant costs for inventory decisions. How are these costs sought
to be controlled with the O. R. techniques? [6]
(b) A baking company sells one of its types of cake by weight. It makes a profit
of 95 paise a pound on every pound of cake sold on the day it is baked. It
disposes of all cakes not sold on the day they are baked at a loss of 15 paise
a pound. If demand is known to have probability density function:
f(R) = 0.03 - 0.0003R,
find the optimum amount of cake the company should bake daily. [10]
4. (a) Explain ABC analysis. [8]
(b) What are its advantages and limitations, if any. [8]
5. A telephone exchange has two long distance operators. The telephone company
finds that, during the peak load, long distance calls arrive in a poisson fashion at a
an average rate of 15 per hour. The length of service on these calls is approximately
exponentially distributed with mean length of 5 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.
1 of 2
Code No: RR410508 Set No. 1
(b) If the subscriber will wait and serviced in turn, what is the expected waiting
time? Establish the formula used.
6. (a) Define the terms: [8]
i. Normal cost
ii. Crash cost
iii. Normal time
iv. Crash time
(b) Define “Critical path”, “Slack time” and “Dummy activity” with reference to
PERT and CPM. How can uncertainty be incorporated in PERT models. [8]
7. Consider the multiplicative congruential generator under the following circum-
stances [16]
(a) a = 11, m = 16, x0 = 7
(b) a = 11, m = 16, x0 = 8
(c) a = 7, m = 16, x0 = 7
(d) a = 7, m = 16, x0 = 8
Generate enough values in each case to complete a cycle. What inferences can be
drawn? Is maximum period achieved.
8. Discuss why validating a model of computer system might be easier than validating
a military combat model. Assume that the computer system of interest is similar
to an existing one. [16]
? ? ? ? ?
2 of 2
Code No: RR410508 Set No. 2
IV B.Tech I Semester Regular Examinations, November 2006
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 is simplex? Write the steps used in the simplex method. [4]
(b) Express the following L. P. problem in standard from: [12]
Minimize z = x1 - 2x2 + x1
subject to the constraints:
2x1 + 3x2 + 4x3 -4
3x1 + 5x2 + 2x3 -7
x1 0, x2 0 and x3 is unrestricted in sign.
2. Solve the following transportation: [16]
1 2 3 4 Supply
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
Requirement 7 5 3 2
3. (a) What are the types of inventory? Why they are maintained? [6]
(b) A particular item has a demand of 9,000 units/year. The cost of one pro-
curement is Rs. 100 and the holding cost per unit is Rs. 2.40 per year. The
replacement is instaneous and no shortages are allowed determine. [10]
i. the economic lot size
ii. the number of orders per year
iii. the time between orders
iv. total cost per year if the cost of one unit is Rs. 1.
4. Make an ABC analysis for the following items in a store and construct the ABC -
analysis chart [16]
5. (a) Define Queue. Explain briefly the main characteristics of queuing system. [8]
(b) What is queuing problem? Explain the transient and steady states of queuing
system. [8]
6. (a) Define the term direct cost and indirect cost as applicable to cost of a project.
[4]
(b) What do you understand by optimum cost and optimum duration? Draw a
typical cost-duration, curve as applicable to PERT AND CPM. [12]
1 of 2
Code No: RR410508 Set No. 2
7. (a) Explain the role of state descriptor in discrete system simulation [6]
(b) Define the terms [6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) Explain the representation of time in discrete system simulation. [4]
8. Discuss the steps in the development of a useful model of input data with suitable
example. [16]
? ? ? ? ?
2 of 2
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: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Explain the term ’Artificial variable’ and its use in Linear programming. [4]
(b) Solve the following L. P. problem by two - 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 two 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 four 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 di erence in raw material cost and transportation cost,
the profit per unit in rupees di ers 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. What are the costs associated with inventory? Distinguish between deterministic
and stochastic models in inventory theory. [16]
4. (a) State various types of items in inventory control techniques. [6]
(b) The following thirty numbers represent the annual value in thousand of ru-
pees of some thirty items of materials selected at random. Carry out an ABC
analysis and list out the values of ‘A’ items only: [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
1 of 2
Code No: RR410508 Set No. 3
5. Repairing a certain type of machine which breaks down in a given factory consists
of 5 basic steps that must be performed sequentially. The time taken to perform
each of the 5 steps is found to have an exponential distribution with mean 5 minutes
and is independent of other steps. If these machines breakdown in poisson fashion
at an average rate of two per hour and if there is only one repairman, what is the
average idle time for each machine that has broken down? [16]
6. (a) Discuss in brief [8]
i. Dummy activity
ii. Free float
iii. Independent float
iv. Total float
(b) What are the three estimates needed for PERT analysis? How do you use
these estimates to compute the expected activity time and the variance in
activity time? [8]
7. List and discuss various periods in the history of simulation software. [16]
8. What parameters do you consider to compare two system designs. Illustrate.( such
as in a queuing system, perhaps two possible queue disciplines or two possible sets
of servers etc.) [16]
? ? ? ? ?
2 of 2
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: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Define 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 following 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) Define constrained optimization problem in non - linear programming prob-
lem? [8]
(b) Write a short note on Kuhn - Tucker condition [8]
3. (a) Explain the decision rules for a purchase inventory model with two price breaks
[4]
(b) Find the optimal order quantity for a product for which the price breaks are
as follows: [12]
Quantity 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? What are the basis steps in
implementary it? [16]
5. A telephone exchange has two long distance operators. The telephone company
finds that, during the peak load, long distance calls arrive in a poisson fashion at a
an average rate of 15 per hour. The length of service on these calls is approximately
exponentially distributed with mean length of 5 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.
1 of 2
Code No: RR410508 Set No. 4
6. (a) Explain PERT and its importance in network analysis. What are the require-
ments for applications of PERT techniques. [10]
(b) List at the di erences between PERT and CPM [6]
7. (a) Explain the role of state descriptor in discrete system simulation [6]
(b) Define the terms [6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) Explain 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 various probability distributions used in input modeling. [4]
? ? ? ? ?
2 of 2
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