Jawaharlal Nehru Technological University Hyderabad 2006 B.E Computer Science IV / I CSE SET4 REG[ MATHEMATICAL MODELLING AND SIMULATION ] - Question Paper

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
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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. [ Marks 4]
(b) Solve the subsequent 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) describe constrained optimization issue in non - linear programming problem? [Marks8]
(b) Write a short note on Kuhn - Tucker condition [Marks8]
3. (a) discuss the decision rules for a purchase inventory model with 2 price breaks[Marks 4]
(b) obtain the optimal order volume for a product for which the price breaks are as follows: [Marks12]
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? [Marks 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. [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) discuss PERT and its importance in network analysis. elaborate the requirements for applications of PERT techniques. [Marks10]
(b) List at the differences ranging from PERT and CPM [Marks 6]
7. (a) discuss the role of state descriptor in discrete system simulation [Marks 6]
(b) describe the terms [Marks6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) discuss 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 different probability distributions used in input modeling. [Marks 4]
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Earning:   Approval pending.