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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 SET4 REG[ MATHEMATICAL MODELLING AND SIMULATION ] Question paper
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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: 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. [ Marks 4]
(b) Solve the following L. P. P. by simplex method : [Marks 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 problem? [Marks8]
(b) Write a short note on Kuhn - Tucker condition [Marks8]
3. (a) Explain the decision rules for a purchase inventory model with two price breaks[Marks 4]
(b) Find the optimal order quantity for a product for which the price breaks are as follows: [Marks12]
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? [Marks 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. [Marks16]
(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) Explain PERT and its importance in network analysis. What are the requirements for applications of PERT techniques. [Marks10]
(b) List at the differences between PERT and CPM [Marks 6]
7. (a) Explain the role of state descriptor in discrete system simulation [Marks 6]
(b) Define the terms [Marks6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) Explain the representation of time in discrete system simulation. [Marks 4]
8. (a) What is the importance of Histograms in input modeling? How do you construct a Histogram. [Marks12]
(b) List out various probability distributions used in input modeling. [Marks 4]
*******
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