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Code No: 812AK
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R13
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, August - 2017
OPERATIONS RESEARCH
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Time: 3 Hours Max. Marks: 60
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part
B consists of 5 Units. Answer any one full question from each unit. Each
question carries 8 marks and may have a, b, c as sub questions.
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PART - A
5 x 4 Marks =20
- What is the significance of the conditions of variables in LPP? [4]
- Explain how you get multiple solutions in assignment problems. [4]
- List out the assumptions made in solving sequencing problem. [4]
- Define a rectangular game and explain the approaches of solving it. [4]
- Explain various queue configurations. [4]
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PART -B
5 x 8 Marks =40
- Use degeneracy principles to solve the following LPP:
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Maximize Z=3x1 +9x2
Subject to X1 +4x2 <8
X1 + 2X2 < 4
X1, X2>0 [8]
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Sreeja & Co wishes to plant advertising strategy. There are two media under
consideration, Siti cable and Popular channel. Siti cable has a reach of 2000
potential customers and Popular channel has a reach of 3000 potential customers.
The cost per appearance of one minute is Rs. 6000 and Rs. 9000 in Siti and
Popular respectively. The budget of Sreeja is Rs. 80,000 per month. There is an--- Content provided by FirstRanker.com ---
important requirement that the total reach for the income group under Rs. 60,000
per annum should not exceed 3000 potential customers. The reach in Siti cable
and Popular channel for this income group is 300 and 150 potential customers.
How many appearances of one minute advertisements should Sreeja plan so as to
maximise the total reach? Formulate the problem and solve it. [8] -
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A dealer stocks and sells four types of Bicycles namely Atlas, Bharath, Champion,
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Duncan which he may procure from three different suppliers namely Priyanshu,
Qureshi and Raju. His anticipated sales for the bicycles for the coming seasons are
410, 680, 310 and 550 nos. respectively. He can obtain 900 bicycles from Priyanshu
600 from Qureshi and 560 from Raju at suitable prices. The profit per bicycle in for
each supplier is tabulated below
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Type Atlas Bharath Champion Duncan Supplier Priyanshu (P) 21.50 26.00 19.50 21.00 Qureshi (Q) 20.50 24.00 20.00 21.00 Raju (R) 18.00 19.50 19.00 19.50 Formulate the above information as transportation model and obtain initial solution by
North West Corner Rule. [8]
OR
- Sai Nath Institute of Science and Technology (SNIST) is providing transport to its
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students in four routes. There are four parties made their bids as given below.Party Bids in routes (in 000 Rs/month) Koti Secunderabad Mehdipatnam Charminar Pradeep travels 4 5 7 6 Raju & co 10 5 4 4 Harika Bus 3 6 2 5 Lavanya transport 6 4 4 5 The institute wishes to allocate one route to each party. The pradeep travels has
offered a discount of 1000/- on additional route if they are allocated more than one
routes. Find the optimal assignment to minimize their monthly costs. Also check
whether the SNIST has to consider the offer given by pradeep Travels. [8]
- A company has six jobs which go through 3 machines X,Y and Z in order XYZ.
The processing time in minutes for each job on each machine is given as follows.
Find the sequence that minimizes the total elapsed time required to complete the
following tasks [8]Jobs 1 2 3 4 5 6 X 18 12 29 36 13 37 Y 7 12 11 2 6 12 Z 21 12 23 47 28 36 OR
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7. A computer has a large number of electronic tube, that are subject to mortality as
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given below:
Period Age of failure Probability of failure 1 0-100 0.10 2 101-200 0.26 3 201-300 0.35 4 301-400 0.22 5 401-300 0.07 If the tubes are group replaced, the cost of replacement is Rs. 15 per tube. Group
replacement can be done at fixed intervals in the night shift when the computer is
not normally used. Replacement of individuals tubes which fails in services costs
Rs. 60 per tube. How frequently should the tubes be replaced? [8]
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- a) What are the distinguishing features of the dynamic programming approach? How
are they different from the other linear programming approaches?
b) Distinguish between the following with reference to dynamic programming.[4+4]
OR - Solve the following game graphically. [8]
-6 0 6 -3/2 7 -3 -8 2 - The demand for an item is deterministic and constant over a time and it is equal to
600 units per year. The unit per cost of the item is Rs. 50 while the cost of placing
an order is Rs. 5. The inventory carrying cost is 20% of the cost of inventory per--- Content provided by FirstRanker.com ---
annum and the cost of shortage is Re. 1 per unit per month. Find the optimal
ordering quantity when stock outs are permitted. If the stock outs are not
permitted, what would be the loss to the company? [8]
OR - Customers arrive at a box office window being managed by a single individual
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according to a Poisson input process with mean rate of 30 per hour the time
required to serve a customer has an exponential distribution with a mean of 90
seconds. Find the average waiting time of a customer. Also determine the average
number of customers in the system and average queue length. [8]
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