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Posted By: kondapalli Member Level: Gold Posted Date: 06 May 2008
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2007 Jawaharlal Nehru Technological University B.Tech Electronics OPERATIONS RESEARCH Question paper
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1. A company has two bottling plants, one located at Bangalore and the other at
Mysore. Each plant produces three brands of drinks A, B and C. Bangalore plant
can produce (in one day) 1500, 3000 and 2000 bottles of A, B and C respectively.
The capacity of Mysore plant remains, 1500, 1000 and 5,000 bottles per day of A,
B and C respectively. A market survey indicates that during the month of April
there will be demand of 20,000 bottles of A, 40,000 bottles of B and 44,000 bottles
of C. The operating cost per day for the plant at Bangalore is Rs.600/- while the
operating cost /day for the plant at Mysore is Rs.400/- For how many days each
plant be run in April so as to minimize the production cost while still meeting the
demand? [16]
2. Shifttrans Transportation Company has four terminals A, B, C and D. At the start
of first day of week, there are 8, 8, 6 and 3 vehicles available at terminals A,B,C and
D respectively. During the previous night, 2, 12, 5 and 6 vehicles were loaded at
plants P, Q, R and S respectively. The distances (in kms.) between the terminals
and plants are given in the table. Based upon the foregoing information, what
vehicles should be sent to which plants in order to minimizes total distance? [16]
P Q R S
A 22 46 16 40
B 41 15 50 40
C 82 32 48 60
D 40 40 36 30
3. (a) Solve the traveling salesman problem given by the following data : C12 =
20;C13 = 4;C14 = 4;C15 = 10;C23 = 5;C34 = 6;C25 = 10;C35 = 6;C45 = 20,
Where Cij = Cji and there is no route between cities i and j if the value for
Cij is not shown.
(b) Find the sequence that minimizes the total time required in performing the
following jobs on three machines in the order ABC. [8+8]
Job 1 2 3 4 5
Machine A 3 6 2 4 5
Machine B 7 9 13 8 11
Machine C 2 15 11 5 4
4. (a) Briefly explain the reasons for replacement.
(b) The following table gives the running costs /year and resale price of equipment
whose purchase price is Rs.8000.
1 of 2
Code No: NR311303 NR
Year 1 2 3 4 5 6 7 8
Running Cost(Rs.) 2500 2600 2800 3100 3500 3900 4400 5400
Resale Value(Rs.) 6500 5500 4700 4200 3800 3500 3500 3500
i. At what year is replacement due?
ii. If the resale value is zero, will there be any change in the replacement
policy? [4+12]
5. Solve the following game by algebraic method [16]
A
B
1 2
1 -2 -4
2 -1 3
3 1 2
6. In a telephone exchange the arrival of calls follow Poisson distribution, with an
average time of 8 minutes between two consecutive calls. The length of a call is
exponentially distributed with mean 4 minutes. Determine
(a) the probability that a call arriving at the booth will have to wait
(b) The average queue length that forms from time to time
(c) The probability that an arrival will have to wait for more than 10 minutes
before the phone is free?
(d) The hours of a day that the exchange will be in use. [16]
7. (a) What are the relevant costs for inventory decisions? How are they obtained
in real life situations?
(b) The annual demand for a component is 7200 units. The carrying cost is Rs.
500/unit/year. The ordering cost is Rs. 1500/- per order and the shortage
cost is Rs. 2000 / unit / year. Find the optimal values of Economic Order
Quality, maximum inventory, maximum shortage capacity, and cycle time.
[6+10]
8. Solve the following model of the optimal subdividing of a cable of length 10 units
into three parts such that the product of their lengths is maximized, using dynamic
programming technique.
Maximize Z = p1Xp2Xp3
Subjected to p1 + p2 + p3 = 10; p1, p2and p3 0 [16]
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