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Posted Date: 31 Dec 2008 Posted By: vindhya Member Level: Diamond
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2008 Jawaharlal Nehru Technological University Computer Science & Engineering III B.Tech Supplimentary Examinations, Aug/Sep 2008 MATHEMATICAL MODELLING AND SIMULATION Question paper
Code No: RR321502 Set No. 3
III B.Tech Supplimentary Examinations, Aug/Sep 2008
MATHEMATICAL MODELLING AND SIMULATION
(Computer Science & Systems Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) What do you mean by primal and dual problems? Is the number of constraints
in the primal and dual the same? [8]
(b) Obtain the dual of the L. P. P. [8]
Minimize z = x1 + x2 + x3
subject to the constraints:
x1 - 3x2 + 4x3 = 5
x1 + 2x2 3
2x2 - x3 4
x1 0,x2 0 and x3 is unrestricted in sign.
2. A manufacturing company produces two products: Radios and T. V. sets. Sales -
price relationships for these two products are given below:
product Quantity demanded Unit price
Radios 1,500-5 p1 p1
T V sets 3,800-10 p2 p2
The total cost functions for these two products are given by 200x1 + 0.1x2
2and
300x2 + 0.1x2
2 respectively. The production takes places on two assembly lines.
Radio sets are assembled on assembly line I and TV sets assembled on Assembly line
II. Because of the limitations of the assembly - line capacities, the daily production
is limited to no more than 80 radios sets and 60 TV sets. The production of
both types of products requires electronic components. The production of each
of these sets requires five units and six units of electronic equipment components
respectively. The electronic component are supplied by another manufacturer and
the supply is limited to 600 units per day. The company has 160 employees, i.e., the
labour supply amounts to 160 man - days. The production of one unit of radio sets
requires 1 man - day of labour, whereas 2 man - days of labour are required for a
TV set. How many units of radio and TV sets should the company produce in order
to maximize the total profit? Formulate the problem as a non-linear programming
problem. [16]
3. (a) Write a shorts on the following: [6]
i. General inventory
ii. Deterministic inventory
iii. Dynamic inventory.
(b) For a fixed order quantity system, find out
i. economic order quantity
ii. optimum buffer stock
iii. reorder level, for an item to the following data:
Annual consumption D = 10,000 units, cost of one unit = Re. 1.00 C3=
Rs. 12.00
per production run, C1 = Re. 0.24 per unit.
Past lead times: 15 days, 25 days, 13 days, 14 days, 30 days, 17 days.
4. Describe various selective inventory management techniques. Explain how these
techniques can be combined to develop broad policy guidelines for selective control.
[16]
5. With respect to queuing system, explain the following [4x4=16]
(a) Balking
(b) Jockeying
(c) Traffic Intensity
(d) Queue length
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. List out the commonly used parameter estimators for various probability
distributions.
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