Jawaharlal Nehru Technological University Hyderabad 2006 B.E Computer Science mathematical modelling and simulation(MMS) ch- - Question Paper

B 13 28 14 26
C 38 19 18 15
D 19 26 24 10
How should the tasks be allocated 1 to a man, so as to minimize the total
man - hours?
3. (a) discuss E. O. Q and sketch its graph. [6]
(b) obtain the optimum order volume for a product for which the price breaks are
as follows: [10]
volume Unit cost(Rs.)
0  q1 < 500 10.00
500 < q2 9.25
The monthly demand for a product is 200 units, the cost of storage is 2% of unit
cost and the cost of ordering is Rs. 350.
4. discuss M.R.P. with a suitable example. Write a short notes on optimal Replen-
ishment system.
[16]
1 of 2
Code No: RR410508 Set No. 3
5. In a car-wash facility, cars arrive for service according to a poisson distribution with
mean five per hour. The time for washing and cleaning every car varies but is obtained
to follow an exponential distribution with mean 10 minutes per car. The facility
cannot handle more than 1 car at a time and has a total of five parking spaces. [16]
(a) obtain the eective arrival rate
(b) What is the probability that an arriving car will get service immediately upon
arrival?
(c) obtain the expected number of parking spaces occupied.
6. A small maintenance project consists of the subsequent 12 jobs with duration in days.
Summarize the CPM computations in standard tabular form calculating total, free
and independent floats of the jobs. [16]
Job Duration
1-2 2
3-4 3
5-8 5
7-9 4
2-3 7
3-5 5
6-7 8
8-9 1
2-4 3
4-6 3
6-10 4
9-10 7
7. discuss different steps involved in simulation study. [16]
8. explain why validating a model of computer system might be easier than validating
a military combat model. presume that the computer system of interest is similar
to an existing one. [16]
? ? ? ? ?
2 of 2
Code No: RR410508 Set No. 4
IV B.Tech I Semester Supplementary Examinations, March 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
? ? ? ? ?
1. A farm is engaged in breeding pigs. The pigs are fed on different products grown
on the farm. In view of the need to ensure certain nutrient constituents (call them
X, Y and Z), it is necessary to buy additional products, say, A and B. 1 unit
of product A contains 36 units of X, three units of Y and 20 units of Z. 1 unit of
product B contains six units of X, 12 units of Y and 10 units of Z. The maximum
requirement of X, Y and Z is 108 units, 36 units and 100 units respectively. Product
A costs Rs. 20 per unit and product B Rs. 40 per unit. Formulate the above as L.
P. P. to minimize the total cost, and solve the issue by using graphic method.
[16]
2. A company manufacturing air - coolers has 2 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 4 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 dierence in raw material cost and transportation cost,
the profit per unit in rupees diers 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. (a) Derive the E. O. Q. formula for the manufacturing model with shortages [6]
(b) A manufacturing firm has to supply 3,000 units annually to a customer who
does not have enough space for storing the material. There is a contract that
if the supplier fails to supply the material, a penalty of Rs. 40 per unit per
month will be levied. The inventory holding cost amounts to Rs. 20 per unit
per month and the setup cost is Rs. 400 per run. obtain the expected number
of shortages at the end of every scheduling period. [10]
4. (a) State different kinds of items in inventory control techniques. [6]
(b) The subsequent thirty numbers represent the annual value in thousand of ru-
pees of a few thirty items of materials opted at random. Carry out an ABC
analysis and list out the values of ‘A’ items only: [10]
1 of 2
Code No: RR410508 Set No. 4
1 two four nine 75 four 25
3 six 13 two four 12 30
100 two seven 40 15 55 1
11 15 eight 19 one 20 1
3 5
5. A repair shop attended by a single mechanic has an avg. of four customers per hour
who bring small appliances for repair. The mechanic inspects them for defects and
quite often can fix them right away or otherwise render a diagnosis. This takes him
6 minutes on the avg.. Arrivals are poisson and service time has the exponential
distribution. You are needed to [16]
(a) obtain the proportion of time during which the shop is empty.
(b) obtain the probability of finding at lowest 1 customer in the shop.
(c) The avg. number of customers in the system
(d) The avg. time, including service, spent by a customer.
6. discuss the rules of net work construction and Fulkerson’s rule for numbering the
events. [16]
7. Consider the multiplicative congruential generator under the subsequent 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 every case to complete a cycle. What inferences can be
drawn? Is maximum period achieved.
8. (a) Distinguish model verification and validation [4]
(b) discuss conceptual and operational model-building process. [12]
? ? ? ? ?
2 of 2

Earning:   Approval pending.