Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 7th Sem New 2172011 Production Optimization Techniques Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2172011 Date: 03/12/2019
Subject Name: Production Optimization Techniques
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.
MARKS
Q.1 (a) Explain the evolution of modern management. 03
(b) What do you meant by a feasible solution of an LPP? 04
(c) Explain application of linear programming. 07
Q.2 (a) Explain how a profit maximization transportation problem can be converted to
an equivalent cost minimization transportation problem.
03
(b) Find the initial basic feasible solution for given problem by using least cost
method:
D1 D2 D3 D4 Supply
P1 2 3 11 7 6
P2 1 0 6 1 1
P3 5 8 15 9 10
Demand 7 5 3 2
04
(c) Use the Big-M method to solve the following LPP
Maximize Z=5X1+3X2
Subject to constraints,
2X1 + 4X2 ? 12 , 2X1 + 2X2 = 10,
5X1 +2X2 ? 10 and X1 , X2 ?0.
07
OR
(c) Use the two-phase method to solve the following LPP
Minimize Z=X1+X2
Subject to constraints,
2X1 + X2 ? 4 , X1 + 7X2 ? 7 and X1 , X2 ?0.
07
Q.3 (a) What is an assignment problem? Give the applications also. 03
(b) What are the methods used for solving an assignment problem? 04
(c) Apply MODI method to obtain optimal solution of transportation problem:
D1 D2 D3 D4 supply
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14 34
07
OR
Q.3 (a) What is the need of Decision tree analysis? 03
(b) Explain the Kendall?s notation for Queuing models. 04
(c) A travelling salesman has to visit five cities. He wishes to start from a
particular city, visit each city once and then return to his starting point. Suggest
him such that his constraint is fulfilled as well as he consumes least cost.The
travelling cost of each city from a particular city is given below:
A B C D E
A ? 2 5 7 1
B 6 ? 3 8 2
C 8 7 ? 4 7
D 12 4 6 ? 5
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2172011 Date: 03/12/2019
Subject Name: Production Optimization Techniques
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.
MARKS
Q.1 (a) Explain the evolution of modern management. 03
(b) What do you meant by a feasible solution of an LPP? 04
(c) Explain application of linear programming. 07
Q.2 (a) Explain how a profit maximization transportation problem can be converted to
an equivalent cost minimization transportation problem.
03
(b) Find the initial basic feasible solution for given problem by using least cost
method:
D1 D2 D3 D4 Supply
P1 2 3 11 7 6
P2 1 0 6 1 1
P3 5 8 15 9 10
Demand 7 5 3 2
04
(c) Use the Big-M method to solve the following LPP
Maximize Z=5X1+3X2
Subject to constraints,
2X1 + 4X2 ? 12 , 2X1 + 2X2 = 10,
5X1 +2X2 ? 10 and X1 , X2 ?0.
07
OR
(c) Use the two-phase method to solve the following LPP
Minimize Z=X1+X2
Subject to constraints,
2X1 + X2 ? 4 , X1 + 7X2 ? 7 and X1 , X2 ?0.
07
Q.3 (a) What is an assignment problem? Give the applications also. 03
(b) What are the methods used for solving an assignment problem? 04
(c) Apply MODI method to obtain optimal solution of transportation problem:
D1 D2 D3 D4 supply
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14 34
07
OR
Q.3 (a) What is the need of Decision tree analysis? 03
(b) Explain the Kendall?s notation for Queuing models. 04
(c) A travelling salesman has to visit five cities. He wishes to start from a
particular city, visit each city once and then return to his starting point. Suggest
him such that his constraint is fulfilled as well as he consumes least cost.The
travelling cost of each city from a particular city is given below:
A B C D E
A ? 2 5 7 1
B 6 ? 3 8 2
C 8 7 ? 4 7
D 12 4 6 ? 5
07
2
E 1 3 2 8 ?
Q.4 (a) At the coffee shop, the customers arrive at the average interval of 6 minutes
and the average time to serve coffee per person is 5minutes. Calculate:
(1). Counter utilization level;
(2). Average no. of customers in the including at service system;
(3). Average no. of customers in queue.
03
(b) Discuss the various costs involved in an inventory problems. 04
(c) The following information is provided for an item:
Annual usage=12000, Ordering cost=Rs. 60 per order, carrying cost=10%, unit
cost of item = Rs. 10, and lead time 10 days.
Find: (1) EOQ, (2) No. of order per year, (3) Average usage if there are 300
working days per year, (4) safety stock if highest usage rate is 70 units per day,
(5) R. O. L., (6) Average inventory, (7) Inventory carrying cost per year.
07
OR
Q.4 (a) Explain the reasons for incorporating dummy activities in a network diagram.
In what why do these differ from the normal activities?
03
(b) Discuss the types of failure in the context of replacement decisions. 04
(c) Following data gives the average cost of spares per year, overhead cost of
maintenance per year and the resale value of certain equipment whose purchase
price is Rs. 50,000.
Year(n) 1 2 3 4 5
Cost of spares 10,000 12,000 14,000 15,000 17,000
Resale value 40,000 32,000 28,000 25,000 22,000
Overhead cost 5,000 5,000 6,000 6,000 8,000
Determine the optimal period for replacement.
07
Q.5 (a) Discuss in brief: (1) total float, (2) free float. Also Explain their uses in
network.
03
(b) Differentiate PERT & CPM. 04
(c) Find an optimal sequence for the following sequencing problems of four jobs
and five machines, when passing is not allowed. Its processing time(in hour)
is given below:
Job Machine
M1 M2 M3 M4 M5
A 7 5 2 3 9
B 6 6 4 5 10
C 5 4 5 6 8
D 8 3 3 2 6
07
OR
Q.5 (a) Determine given terminology from sequencing problems: (1). Number of
machines, (2) Idle time on a machine, (3) Total elapsed time.
03
(b) What is EMV (expected monetary value)? How it is computed to be used a
criterion of decision making and when?
04
(c) For the given activities determine:
(1). Critical path using PERT
(2). Calculate variance and standard deviation for each activity.
(3). Calculate the probability of completing the project in 26 days.
Activity to tm tp
1-2 6 9 12
1-3 3 4 11
2-4 2 5 14
3-4 4 6 8
3-5 1 1.5 5
2-6 5 6 7
4-6 7 8 15
5-6 1 2 3
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2172011 Date: 03/12/2019
Subject Name: Production Optimization Techniques
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.
MARKS
Q.1 (a) Explain the evolution of modern management. 03
(b) What do you meant by a feasible solution of an LPP? 04
(c) Explain application of linear programming. 07
Q.2 (a) Explain how a profit maximization transportation problem can be converted to
an equivalent cost minimization transportation problem.
03
(b) Find the initial basic feasible solution for given problem by using least cost
method:
D1 D2 D3 D4 Supply
P1 2 3 11 7 6
P2 1 0 6 1 1
P3 5 8 15 9 10
Demand 7 5 3 2
04
(c) Use the Big-M method to solve the following LPP
Maximize Z=5X1+3X2
Subject to constraints,
2X1 + 4X2 ? 12 , 2X1 + 2X2 = 10,
5X1 +2X2 ? 10 and X1 , X2 ?0.
07
OR
(c) Use the two-phase method to solve the following LPP
Minimize Z=X1+X2
Subject to constraints,
2X1 + X2 ? 4 , X1 + 7X2 ? 7 and X1 , X2 ?0.
07
Q.3 (a) What is an assignment problem? Give the applications also. 03
(b) What are the methods used for solving an assignment problem? 04
(c) Apply MODI method to obtain optimal solution of transportation problem:
D1 D2 D3 D4 supply
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14 34
07
OR
Q.3 (a) What is the need of Decision tree analysis? 03
(b) Explain the Kendall?s notation for Queuing models. 04
(c) A travelling salesman has to visit five cities. He wishes to start from a
particular city, visit each city once and then return to his starting point. Suggest
him such that his constraint is fulfilled as well as he consumes least cost.The
travelling cost of each city from a particular city is given below:
A B C D E
A ? 2 5 7 1
B 6 ? 3 8 2
C 8 7 ? 4 7
D 12 4 6 ? 5
07
2
E 1 3 2 8 ?
Q.4 (a) At the coffee shop, the customers arrive at the average interval of 6 minutes
and the average time to serve coffee per person is 5minutes. Calculate:
(1). Counter utilization level;
(2). Average no. of customers in the including at service system;
(3). Average no. of customers in queue.
03
(b) Discuss the various costs involved in an inventory problems. 04
(c) The following information is provided for an item:
Annual usage=12000, Ordering cost=Rs. 60 per order, carrying cost=10%, unit
cost of item = Rs. 10, and lead time 10 days.
Find: (1) EOQ, (2) No. of order per year, (3) Average usage if there are 300
working days per year, (4) safety stock if highest usage rate is 70 units per day,
(5) R. O. L., (6) Average inventory, (7) Inventory carrying cost per year.
07
OR
Q.4 (a) Explain the reasons for incorporating dummy activities in a network diagram.
In what why do these differ from the normal activities?
03
(b) Discuss the types of failure in the context of replacement decisions. 04
(c) Following data gives the average cost of spares per year, overhead cost of
maintenance per year and the resale value of certain equipment whose purchase
price is Rs. 50,000.
Year(n) 1 2 3 4 5
Cost of spares 10,000 12,000 14,000 15,000 17,000
Resale value 40,000 32,000 28,000 25,000 22,000
Overhead cost 5,000 5,000 6,000 6,000 8,000
Determine the optimal period for replacement.
07
Q.5 (a) Discuss in brief: (1) total float, (2) free float. Also Explain their uses in
network.
03
(b) Differentiate PERT & CPM. 04
(c) Find an optimal sequence for the following sequencing problems of four jobs
and five machines, when passing is not allowed. Its processing time(in hour)
is given below:
Job Machine
M1 M2 M3 M4 M5
A 7 5 2 3 9
B 6 6 4 5 10
C 5 4 5 6 8
D 8 3 3 2 6
07
OR
Q.5 (a) Determine given terminology from sequencing problems: (1). Number of
machines, (2) Idle time on a machine, (3) Total elapsed time.
03
(b) What is EMV (expected monetary value)? How it is computed to be used a
criterion of decision making and when?
04
(c) For the given activities determine:
(1). Critical path using PERT
(2). Calculate variance and standard deviation for each activity.
(3). Calculate the probability of completing the project in 26 days.
Activity to tm tp
1-2 6 9 12
1-3 3 4 11
2-4 2 5 14
3-4 4 6 8
3-5 1 1.5 5
2-6 5 6 7
4-6 7 8 15
5-6 1 2 3
07
3
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This post was last modified on 20 February 2020