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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABADMCA 1I Semester Examinations, April/May - 2019
OPERATIONS RESEARCH
Time: 3hrs Max.Marks:75
Note: This question paper contains two parts A and B.
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Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part Bconsists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A
5 x 5 Marks =25
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- a) Define feasible, Infeasible solution and no solution. 5
b) State the mathematical formulation for T.P. 5
c) List two uses of replacement model. 5
d) Explain minimax principle used in the theory of games. 5
e) Explain characteristics and classification of queuing models. 5
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PART -B
5 x 10 Marks =50
- a) The ABC Company has been a producer of picture tubes for television sets and certain
printed circuits for radios. The company has just explained into full scale production
and marketing of AM and AM-FM radios. It has built a new plant that can operate 48--- Content provided by FirstRanker.com ---
hours per week. Production of an AM radio in the new plant will require 2 hours and
production of an AM-FM radio will require 3 hours. Each AM radio will contribute Rs.
40 to profits while an AM-FM radio will contribute Rs. 80 to profits. The marketing
departments, after extensive research, have determined that a maximum of 15 AM
radios and 10 AM-FM radios can be sold each week. Formulate the LPP.--- Content provided by FirstRanker.com ---
b) Solve by Big M method
Maximize Z=3x1-x2
Subject to
2x1+X2 >= 2,
X1 <= 3,--- Content provided by FirstRanker.com ---
X1, X2 >=0 [5+5]
OR - a) Write the steps for solving Linear Programming Problem by Graphical method. State its
limitations.
b) Solve the following LP problems graphically--- Content provided by FirstRanker.com ---
Minimize Z =3 x1 + 2 X2
Subject to
5 X1 + X2 >= 10,
X1 + X2 >= 6,
X1 +4 X2 >= 12--- Content provided by FirstRanker.com ---
X1 ,X2>= 0 [5+5]
- a) Determine an IBFS by Vogel’s Approximation method and also find the optimum
solution.
Source D1 D2 D3 D4 Supply--- Content provided by FirstRanker.com ---
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14 [10]
OR - A departmental has five employees with five jobs to be performed. The time (in hours)
each men will take to perform each job is given in the effectiveness matrix.
How should the jobs be allocated, one per employee, so as to minimize the total
man-hours.
Employees--- Content provided by FirstRanker.com ---
jobs 1 2 3 4 5
a 10 5 13 15 16
b 3 9 18 13 6
c 10 7 2 2 2
d 11 9 7 12 12--- Content provided by FirstRanker.com ---
e 7 9 10 4 12 [10]
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- Machine B costs Rs.10,000. Annual operating costs are Rs.400 for the first year, and
then increased by Rs.800 every year. You know have a machine of type A which is one
year old. Should you replace it with B, if so, when? [10]
OR - The following failure rates have been observed for a certain type of light bulbs:
End of the week : 1 2 3 4 5 6 7 8
Probability
Of failure to date : 0.05 0.13 0.25 0.43 0.68 0.88 0.96 1.00
The cost of replacing an individual failed bulb is Rs.1.50. The decision is made to--- Content provided by FirstRanker.com ---
replace all bulbs simultancously at fixed intervals, and also to replace individual bulbs
as they fail in service. -If the cost of group replacement is 30 paise per bulb, what is the
best interval between group replacements? At what group replacement price per bulb
would a policy of strictly individual replacement become preferable to the adopted
policy? [10]
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- Explain Principal of optimality, state and stage in the context of dynamic programming.
Solve the following Two-person zero sum game using graphical technique [5+5]
Player B
I II
I 2 4--- Content provided by FirstRanker.com ---
Player A II -1 6
III 3 5
IV 4 1
V 3 4
VI -7 6--- Content provided by FirstRanker.com ---
OR - Use dominance property to reduce the game to 2x2 game and hence find optimal
strategies.
Player B
I II III IV--- Content provided by FirstRanker.com ---
I 5 -10 9 0
Player A II 6 7 3 1
III 8 7 15 1
IV 3 4 -1 4 [10]
- A company uses annually 48,000 units of a raw material costing Rs.120/- unit placing
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each order costs Rs.45/- carrying cost is 1.5% per year of the average inventory. Find
E.O.Q and minimum cost. - A self-service store employs one cashier at its counter. Nine customers arrive on an
average every 5 minutes while the cashier can serve 10 customers in 5 minutes.
Assuming Poisson distribution for arrival rate and exponential distribution for service--- Content provided by FirstRanker.com ---
time, find
1) Average number of customers in the system.
ii) Average number of customers in the queue or average queue length. [5+5]
OR - A motor manufacturing company purchases 10,000 items of certain motor parts for its
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annual requirements, ordering one month usage at a time. Each spare costs Rs.20, the
Ordering cost per order if Rs.15 and carrying charges are 10% of the unit item cost per
year. Make a more economical purchasing policy:
A branch of Punjab National Bank has only one typist. Since the typing work varies in
length (number of pages to be typed) the typing rate is randomly distributed--- Content provided by FirstRanker.com ---
approximating of Poisson distribution with’'mean rate of 8 letters per hour. The letters
arrive at a rate of 5 per hour during the entire 8-hour work day. If the typewriter is
valued at Rs. 1.50 per hour, determine
1) Equipment utilization
ii) The percent time that an arriving letter has to wait. [5+5]
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