Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 7th Sem Old 171901 Operation Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (OLD) EXAMINATION ? WINTER 2018
Subject Code: 171901 Date: 06/12/2018
Subject Name: Operation Research
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) (i) Describe the various objectives of OR? Write any two merits of OR. 04
(ii) What is degeneracy in transportation? How it resolve? 03
(b) Using Graphical method, Find the maximum value of
Z = 2X1+X2
Subjected to, X1 + 2X2 ? 10,
X1 + X2 ? 6,
X1 ? 2X2 ? 1,
X1 ? X2 ? 2,
X1, X2 ? 0
07
Q.2 (a) Find initial feasible solution by VAM and check optimality by MODI, where cell
entries are unit costs.
D1 D2 D3 D4 D5 Available
O1 68 35 4 74 15 18
O2 57 88 91 3 8 17
O3 91 60 75 45 60 19
O4 52 53 24 7 82 13
O5 51 18 82 13 7 15
Required 16 18 20 14 14
07
(b) Using Simplex method,
Maximize, Z = 3X1 ? X2
Subjected to, 2X1 + X2 ? 2,
X1 + 3X2 ? 3,
X2 ? 4,
X1, X2 ? 0
07
OR
(b) Formulate the LPP and prepare initial table, if An Air Force is experimenting
with three types of bombs P, Q and R in which three kinds of explosives, viz. A,
B and C will be used. Taking the various factors into account, it has been decided
to use the maximum 600 kg of explosive A. at least 480 kg of explosive B and
exactly 540 kg of explosive C. Bomb P requires 3, 2, 2 kg, Bomb Q requires 1,
4, 3 kg and Bomb R requires 4, 2, 3 kg of explosives A, B and C respectively.
Bomb P is estimated to give the equivalent of a 2 ton explosive, bomb Q, a 3 ton
07
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (OLD) EXAMINATION ? WINTER 2018
Subject Code: 171901 Date: 06/12/2018
Subject Name: Operation Research
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) (i) Describe the various objectives of OR? Write any two merits of OR. 04
(ii) What is degeneracy in transportation? How it resolve? 03
(b) Using Graphical method, Find the maximum value of
Z = 2X1+X2
Subjected to, X1 + 2X2 ? 10,
X1 + X2 ? 6,
X1 ? 2X2 ? 1,
X1 ? X2 ? 2,
X1, X2 ? 0
07
Q.2 (a) Find initial feasible solution by VAM and check optimality by MODI, where cell
entries are unit costs.
D1 D2 D3 D4 D5 Available
O1 68 35 4 74 15 18
O2 57 88 91 3 8 17
O3 91 60 75 45 60 19
O4 52 53 24 7 82 13
O5 51 18 82 13 7 15
Required 16 18 20 14 14
07
(b) Using Simplex method,
Maximize, Z = 3X1 ? X2
Subjected to, 2X1 + X2 ? 2,
X1 + 3X2 ? 3,
X2 ? 4,
X1, X2 ? 0
07
OR
(b) Formulate the LPP and prepare initial table, if An Air Force is experimenting
with three types of bombs P, Q and R in which three kinds of explosives, viz. A,
B and C will be used. Taking the various factors into account, it has been decided
to use the maximum 600 kg of explosive A. at least 480 kg of explosive B and
exactly 540 kg of explosive C. Bomb P requires 3, 2, 2 kg, Bomb Q requires 1,
4, 3 kg and Bomb R requires 4, 2, 3 kg of explosives A, B and C respectively.
Bomb P is estimated to give the equivalent of a 2 ton explosive, bomb Q, a 3 ton
07
2
explosive and R, a 4 ton explosive respectively. Under what production schedule
can the Air Force make the biggest bang?
Q.3 (a) Four different jobs can be done on four different machines. The set-up and take-
down time costs are assumed to be prohibitively high for changeovers. The
matrix below gives the cost in rupees of producing jobs i on machine j.
M1 M2 M3 M4
J1 5 7 11 6
J2 8 5 9 6
J3 4 7 10 7
J4 10 4 8 3
How should the jobs be assigned to the various machines so that the total cost is
minimized?
07
(b) Explain Kendall?s notation for queuing system. Also explain the term: Balking
and Jockeying.
07
OR
Q.3 (a) Five wagons are available at stations 1, 2, 3, 4 and 5. These are required at five
stations I, II, III, IV and V. The mileages between various stations are given by
the table below. How should the wagons be transported so as to minimize the
total mileage covered?
I II III IV V
1 10 5 9 18 11
2 13 9 6 12 14
3 3 2 4 4 5
4 18 9 12 17 15
5 11 6 14 19 10
07
(b) A company uses Rs. 10,000 worth of an item during the year. The ordering costs
are Rs. 25 per order and carrying charges are 12.5% of the average inventory
value. Find the economic order quantity, number of orders per year, time period
per order and the total cost.
07
Q.4 (a) The maintenance cost and resale value per year of a machine whose purchase
price is Rs. 7000 is given below.
Year 1 2 3 4 5 6 7 8
Maintenance cost
in Rs.
900 1200 1600 2100 2800 3700 4700 5900
Resale value in Rs. 4000 2000 1200 600 500 400 400 400
When should the machine be replaced?
07
(b) A company currently involved in negotiation with its union on the upcoming
wage contract. Positive sign in below table represents wage increase while
negative sign represents wage reduction. What are the optimal strategies for the
company as well as the union? What is the game value?
07
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (OLD) EXAMINATION ? WINTER 2018
Subject Code: 171901 Date: 06/12/2018
Subject Name: Operation Research
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) (i) Describe the various objectives of OR? Write any two merits of OR. 04
(ii) What is degeneracy in transportation? How it resolve? 03
(b) Using Graphical method, Find the maximum value of
Z = 2X1+X2
Subjected to, X1 + 2X2 ? 10,
X1 + X2 ? 6,
X1 ? 2X2 ? 1,
X1 ? X2 ? 2,
X1, X2 ? 0
07
Q.2 (a) Find initial feasible solution by VAM and check optimality by MODI, where cell
entries are unit costs.
D1 D2 D3 D4 D5 Available
O1 68 35 4 74 15 18
O2 57 88 91 3 8 17
O3 91 60 75 45 60 19
O4 52 53 24 7 82 13
O5 51 18 82 13 7 15
Required 16 18 20 14 14
07
(b) Using Simplex method,
Maximize, Z = 3X1 ? X2
Subjected to, 2X1 + X2 ? 2,
X1 + 3X2 ? 3,
X2 ? 4,
X1, X2 ? 0
07
OR
(b) Formulate the LPP and prepare initial table, if An Air Force is experimenting
with three types of bombs P, Q and R in which three kinds of explosives, viz. A,
B and C will be used. Taking the various factors into account, it has been decided
to use the maximum 600 kg of explosive A. at least 480 kg of explosive B and
exactly 540 kg of explosive C. Bomb P requires 3, 2, 2 kg, Bomb Q requires 1,
4, 3 kg and Bomb R requires 4, 2, 3 kg of explosives A, B and C respectively.
Bomb P is estimated to give the equivalent of a 2 ton explosive, bomb Q, a 3 ton
07
2
explosive and R, a 4 ton explosive respectively. Under what production schedule
can the Air Force make the biggest bang?
Q.3 (a) Four different jobs can be done on four different machines. The set-up and take-
down time costs are assumed to be prohibitively high for changeovers. The
matrix below gives the cost in rupees of producing jobs i on machine j.
M1 M2 M3 M4
J1 5 7 11 6
J2 8 5 9 6
J3 4 7 10 7
J4 10 4 8 3
How should the jobs be assigned to the various machines so that the total cost is
minimized?
07
(b) Explain Kendall?s notation for queuing system. Also explain the term: Balking
and Jockeying.
07
OR
Q.3 (a) Five wagons are available at stations 1, 2, 3, 4 and 5. These are required at five
stations I, II, III, IV and V. The mileages between various stations are given by
the table below. How should the wagons be transported so as to minimize the
total mileage covered?
I II III IV V
1 10 5 9 18 11
2 13 9 6 12 14
3 3 2 4 4 5
4 18 9 12 17 15
5 11 6 14 19 10
07
(b) A company uses Rs. 10,000 worth of an item during the year. The ordering costs
are Rs. 25 per order and carrying charges are 12.5% of the average inventory
value. Find the economic order quantity, number of orders per year, time period
per order and the total cost.
07
Q.4 (a) The maintenance cost and resale value per year of a machine whose purchase
price is Rs. 7000 is given below.
Year 1 2 3 4 5 6 7 8
Maintenance cost
in Rs.
900 1200 1600 2100 2800 3700 4700 5900
Resale value in Rs. 4000 2000 1200 600 500 400 400 400
When should the machine be replaced?
07
(b) A company currently involved in negotiation with its union on the upcoming
wage contract. Positive sign in below table represents wage increase while
negative sign represents wage reduction. What are the optimal strategies for the
company as well as the union? What is the game value?
07
3
Conditional costs to the company (Rs. In lakhs)
Union Strategies
U1 U2 U3 U4
C1 +0.25 +0.27 +0.35 -0.02
Company
C2 +0.20 +0.16 +0.08 +0.08
Strategies
C3 +0.14 +0.12 +0.15 +0.13
C4 +0.30 +0.14 +0.19 +0.00
OR
Q.4 (a) A Hand Drill Machine costs Rs. 9000. Annual operating costs are Rs. 200 for the
first year, and then increase by Rs. 2000 every year. Determine the best age at
which to replace the machine. If the optimum replacement policy is followed,
what will be the average yearly cost of owning and operating the machine?
Assume that the machine has no resale value when replaced and that future costs
are not discounted.
07
(b) Explain the following: (i) Minimax and Maximin principles (ii) Pure and mixed
strategies (iii) Two-person zero-sum game.
07
Q.5 (a) Estimated times for the jobs of a project are given below:
Job: A B C D E F G H I J K L
Time
(weeks)
13 5 8 10 9 7 7 12 8 9 4 17
The constraints governing the jobs are as follows:
A and B are start jobs; A controls C, D and E; B controls F and J; G depends
upon C; H depends on D; E and F control I and L; K follows J; L is also controlled
by K; G, H, I and L are the last jobs. Draw the network, determine float for each
activity, project duration and the critical path.
07
(b) Explain Monte Carlo method and give the situations where these methods are
useful.
07
OR
Q.5 (a) What do you mean by floats? Explain how to calculate each type of floats with
respect to CPM?
07
(b) Explain the Bellman?s principle of optimality with illustrative example. 07
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This post was last modified on 20 February 2020