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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, October / November - 2020
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OPERATIONS RESEARCHTime: 2 Hours
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Max.Marks:75
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Answer any five questionsAll questions carry equal marks
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1.
Old hens can be brought at Rs 20 each and young ones at Rs. 50 each. The old hens lay 3
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eggs per week and the young ones lay 5 eggs per week, each egg being worth of Rs. 1.50ps. A hen (young or old) costs Rs. 1.50 per week to feed; I have only Rs. 800 to spend for
hens. How many of each kind should I buy to give a profit of at least Rs.60/- per week,
assuming that I cannot house more than 20 hens? Formulate and solve by simplex
Method.
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2.
ABC agency transports material from one place to the other on commission basis. The
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following are the estimated commissions per unit of material to be transported from theplants P
used
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1, P2 and P3 to market centers M1, M2 and M3. Optimize the commissions to beearned by the agency (note that there is no route available to transport from P2 to M1)
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M1
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M2 M3 Supply
P
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1
6
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9
8
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120P
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2
-
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42
80
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P
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311
5
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4
80
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Demand 150 7060
280
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3.
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There are six jobs, each of which must go through machines A, B and C. Processing time(in hours) are given in the following table
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Job
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12
3
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4
5
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6Machine A 12
10
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9
14
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79
Machine B
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7
6
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65
4
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4
Machine C
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65
6
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4
2
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4Order of the processing of each job is ACB. Find the sequence and the total time elapsed
also find idle time for each machine.
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[15]4.
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A computer has a 1000 number of electronic tube, that is subject to mortality as given
below:
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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?
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S OCT 2020
5.
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In a bank cheques are cashed at a single teller counter. Customers arrive at the counter in
a Poisson manner at an average rate of 30 customers per hour. The teller takes on an
average a minute and a half to cash cheque. The service time has been shown to be
exponentially distributed.
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a) Calculate the % of time the teller is busy andb) Also calculate the average time a customer is expected to wait.
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[15]6.
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Dr. Raju's out ? patient clinic can accommodate six people only in the waiting hall, the
patients who arrive when hall is full, balk away. The patients arrive in poisson fashion at
an average rate of 3 per hour and spend an average of 15 minutes in Doctor's chamber
which is exponentially distributed. Find
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a) The probability that a patient can get directly into the doctor's chamber upon his armb) Expected number of patients waiting for treatment.
c) The probability that there are more than 5 patients.
d) The time a patient can expect to spend in the clinic
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7.
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The demand of an item is uniform at a rate of 20 units per month. The fixed cost is Rs. 10
each time a production run is made. The production cost is Rs 1 per item and the
used
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inventory carrying cost is Rs. 0.25 per item per month. If the shortage cost is Rs. 1.25 per
item per month, determine how often to make a production run and of what size should it
be?
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8.
Solve the following LPP by dynamic programming Method:
Max Z = 2x1+5x2
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Subject to constraint
2x1+x2 430
2x2 460
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x1,x2 0.
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