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Posted By: Sri Member Level: Gold Posted Date: 18 Nov 2007
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2006 Jawaharlal Nehru Technological University B.E Computer Science IV / I CSE SET1 REG[ MATHEMATICAL MODELLING AND SIMULATION ] 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. [Marks6]
(b) Find all basic solutions for the problem [Marks10]
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. [Marks 4]
(b) Find the optimal integer solution to the following all L.P. P. [Marks12]
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? [Marks 6]
(b) A baking company sells one of its types of cake by weight. It makes a profit of 95 paisa 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 paisa 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. [Marks10]
4. (a) Explain ABC analysis. [Marks 8]
(b) What are its advantages and limitations, if any. [Marks 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. [Marks 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.
6. (a) Define the terms: [Marks 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. [Marks 8]
7. Consider the multiplicative congruential generator under the following circumstances [Marks 16]
(a) a = 11, m = 16, x0 = 7
(b) a = 11, m = 16, x0 = 8
(c) a = 07, m = 16, x0 = 7
(d) a = 07, 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.
[Marks16]
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