Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 7th Sem New 21720042172011 Production Optimization Techniques Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2172004/2172011 Date:27/05/2019
Subject Name:Production Optimization Techniques
Time:02:30 PM TO 05:00 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) Explain and illustrate the following principles of decision making:
(a) Laplace (b) Maximin (c) Maxima
03
(b) Answer the following questions:
1. The key column indicates
(a) Outgoing variable (b) Incoming variable,
(c) Independent variable (d) Dependent variable
2. The total number of allocation in a basic feasible solution of
transportation problem of
m ? n size is equal to
(a) m ? n (b) (m / n ) ? 1
(c) m + n +1 (d) m + n ? 1
3. When money value changes with time at 10 %, then Present Worth
Factor (PWF) for first year is :
(a) 1 (b) 0.909
(c) 0.852 (d) 0.9
4. At EOQ
(a) Annual purchase cost =
Annual ordering cost
(b) Annual ordering cost =
Annual carrying cost
(c) Annual carrying cost =
Annual shortage cost
(d) Annual shortage cost =
Annual purchase cost
04
(c) Solve LPP using simplex method.
Minimize Z = 8x + 10y
Subject to : 3x + 9y ? 100
8x + 4y ? 150
x , y ? 0
07
Q.2 (a) Explain the following terms related to queuing theory.
1. Queue length 2. System length 3. Waiting time in queue
03
(b) A company manufactures two products X and Y whose profit contributions are Rs.10
and Rs. 20 respectively. Product X requires 5 hours on machine I, 3 hours on
machine II and 2 hours on machine III. The requirement of product Y is 3 hours on
machine I, 6 hours on machine II and 5 hours on machine III. The available
capacities for the planning period for machine I, II and III are 30, 36 and 20 hours
respectively. Formulate above LPP to maximize the profit. Also write the
standardize form of this LPP.
04
(c) Solve following transportation problem:
Origin A B C Availability
X 2 1 2 20
Y 3 4 1 40
Requirement 20 15 25
07
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Page 1 of 3
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2172004/2172011 Date:27/05/2019
Subject Name:Production Optimization Techniques
Time:02:30 PM TO 05:00 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) Explain and illustrate the following principles of decision making:
(a) Laplace (b) Maximin (c) Maxima
03
(b) Answer the following questions:
1. The key column indicates
(a) Outgoing variable (b) Incoming variable,
(c) Independent variable (d) Dependent variable
2. The total number of allocation in a basic feasible solution of
transportation problem of
m ? n size is equal to
(a) m ? n (b) (m / n ) ? 1
(c) m + n +1 (d) m + n ? 1
3. When money value changes with time at 10 %, then Present Worth
Factor (PWF) for first year is :
(a) 1 (b) 0.909
(c) 0.852 (d) 0.9
4. At EOQ
(a) Annual purchase cost =
Annual ordering cost
(b) Annual ordering cost =
Annual carrying cost
(c) Annual carrying cost =
Annual shortage cost
(d) Annual shortage cost =
Annual purchase cost
04
(c) Solve LPP using simplex method.
Minimize Z = 8x + 10y
Subject to : 3x + 9y ? 100
8x + 4y ? 150
x , y ? 0
07
Q.2 (a) Explain the following terms related to queuing theory.
1. Queue length 2. System length 3. Waiting time in queue
03
(b) A company manufactures two products X and Y whose profit contributions are Rs.10
and Rs. 20 respectively. Product X requires 5 hours on machine I, 3 hours on
machine II and 2 hours on machine III. The requirement of product Y is 3 hours on
machine I, 6 hours on machine II and 5 hours on machine III. The available
capacities for the planning period for machine I, II and III are 30, 36 and 20 hours
respectively. Formulate above LPP to maximize the profit. Also write the
standardize form of this LPP.
04
(c) Solve following transportation problem:
Origin A B C Availability
X 2 1 2 20
Y 3 4 1 40
Requirement 20 15 25
07
Page 2 of 3
OR
(c) Discuss various methods to find the initial feasible solution of transportation
problem
07
Q.3 (a) How can you formulate an assignment problem as a standard linear programming
problem? Illustrate.
03
(b) What is the significance of the duality theory of linear programming? Describe the
general rule for writing the dual of linear programming problem.
04
(c) State and discuss the methods employed for solving an assignment problem. 07
OR
Q.3 (a) With the help of quantity cost curve, explain the significance of EOQ. What are the
limitation of using the formula for an EOQ?
03
(b) How would you deal with the assignment problems where
1. Some assignments are prohibited?
2. The objective function is of maximization type?
04
(c) What is queuing theory? Explain the general structure of the queuing system.
Illustrate some queuing situations.
07
Q.4 (a) Information on activities required for a project is as follows:
Name A B C D E F G H I J K
Activities
Node
1-2 1-3 1-4 2-5 3-5 3-6 3-7 4-6 5-7 6-8 7-8
Duration
days
2 7 8 3 6 10 4 6 2 5 6
Draw the network diagram and earliest and latest times.
07
(b) Determine Total float and free floats for above network (Q 4 (a)). 04
(c) What are the major comparative characteristics of the PERT and CPM model? What are
their limitations, if any? Discuss.
03
OR
Q.4 (a) The following table shows, for each activity of project, the normal and crash time
as also normal and crash costs. The contract includes a penalty clause of Rs. 200
per day in excess of 19 days. The overhead cost is Rs 400 per day.
Activity
Time (Days) Cost (Rs)
Normal Crash Normal Crash
1-2 6 4 600 1000
1-3 4 2 600 1400
2-4 5 3 500 1500
2-5 3 1 450 650
3-4 6 4 900 2000
4-6 8 4 800 3000
5-6 4 2 400 1000
6-7 3 2 450 800
Draw the project network.
04
(b) Determine critical path and cost of completing project in normal time. 03
(c) Crash the project activities and determine the cost of completing the project in the
minimum time.
07
Q.5 (a) Explain briefly the difference in replacement policies of items which deteriorate
gradually and items which fail completely.
03
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Page 1 of 3
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2172004/2172011 Date:27/05/2019
Subject Name:Production Optimization Techniques
Time:02:30 PM TO 05:00 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) Explain and illustrate the following principles of decision making:
(a) Laplace (b) Maximin (c) Maxima
03
(b) Answer the following questions:
1. The key column indicates
(a) Outgoing variable (b) Incoming variable,
(c) Independent variable (d) Dependent variable
2. The total number of allocation in a basic feasible solution of
transportation problem of
m ? n size is equal to
(a) m ? n (b) (m / n ) ? 1
(c) m + n +1 (d) m + n ? 1
3. When money value changes with time at 10 %, then Present Worth
Factor (PWF) for first year is :
(a) 1 (b) 0.909
(c) 0.852 (d) 0.9
4. At EOQ
(a) Annual purchase cost =
Annual ordering cost
(b) Annual ordering cost =
Annual carrying cost
(c) Annual carrying cost =
Annual shortage cost
(d) Annual shortage cost =
Annual purchase cost
04
(c) Solve LPP using simplex method.
Minimize Z = 8x + 10y
Subject to : 3x + 9y ? 100
8x + 4y ? 150
x , y ? 0
07
Q.2 (a) Explain the following terms related to queuing theory.
1. Queue length 2. System length 3. Waiting time in queue
03
(b) A company manufactures two products X and Y whose profit contributions are Rs.10
and Rs. 20 respectively. Product X requires 5 hours on machine I, 3 hours on
machine II and 2 hours on machine III. The requirement of product Y is 3 hours on
machine I, 6 hours on machine II and 5 hours on machine III. The available
capacities for the planning period for machine I, II and III are 30, 36 and 20 hours
respectively. Formulate above LPP to maximize the profit. Also write the
standardize form of this LPP.
04
(c) Solve following transportation problem:
Origin A B C Availability
X 2 1 2 20
Y 3 4 1 40
Requirement 20 15 25
07
Page 2 of 3
OR
(c) Discuss various methods to find the initial feasible solution of transportation
problem
07
Q.3 (a) How can you formulate an assignment problem as a standard linear programming
problem? Illustrate.
03
(b) What is the significance of the duality theory of linear programming? Describe the
general rule for writing the dual of linear programming problem.
04
(c) State and discuss the methods employed for solving an assignment problem. 07
OR
Q.3 (a) With the help of quantity cost curve, explain the significance of EOQ. What are the
limitation of using the formula for an EOQ?
03
(b) How would you deal with the assignment problems where
1. Some assignments are prohibited?
2. The objective function is of maximization type?
04
(c) What is queuing theory? Explain the general structure of the queuing system.
Illustrate some queuing situations.
07
Q.4 (a) Information on activities required for a project is as follows:
Name A B C D E F G H I J K
Activities
Node
1-2 1-3 1-4 2-5 3-5 3-6 3-7 4-6 5-7 6-8 7-8
Duration
days
2 7 8 3 6 10 4 6 2 5 6
Draw the network diagram and earliest and latest times.
07
(b) Determine Total float and free floats for above network (Q 4 (a)). 04
(c) What are the major comparative characteristics of the PERT and CPM model? What are
their limitations, if any? Discuss.
03
OR
Q.4 (a) The following table shows, for each activity of project, the normal and crash time
as also normal and crash costs. The contract includes a penalty clause of Rs. 200
per day in excess of 19 days. The overhead cost is Rs 400 per day.
Activity
Time (Days) Cost (Rs)
Normal Crash Normal Crash
1-2 6 4 600 1000
1-3 4 2 600 1400
2-4 5 3 500 1500
2-5 3 1 450 650
3-4 6 4 900 2000
4-6 8 4 800 3000
5-6 4 2 400 1000
6-7 3 2 450 800
Draw the project network.
04
(b) Determine critical path and cost of completing project in normal time. 03
(c) Crash the project activities and determine the cost of completing the project in the
minimum time.
07
Q.5 (a) Explain briefly the difference in replacement policies of items which deteriorate
gradually and items which fail completely.
03
Page 3 of 3
(b) There are seven jobs, each of which has to go through the machines A and B in the
order AB. Processing times in hours are as follows:
Job 1 2 3 4 5 6 7
Machine
A
3 12 15 6 10 11 9
Machine
B
8 10 10 6 12 1 3
Determine a sequence of these jobs that will minimize the elapsed time T. Also find
T.
04
(c) A client has an estate agent to sell three properties A, B and C for him and agrees to
pay him 5% commission on each sale. He specifies certain conditions. The estate
agent must sell property A first, and this he must do within 60 days. If and when A
is sold the agent receives his 5% commission on that sale. He can then either back
out at this stage or nominate and try to sell one of the remaining two properties
within 60 days. If he does not succeed in selling the nominated property in that
period, he is not given opportunity to sell the third property on the same conditions.
The prices, selling costs (incurred by the estate agent whenever a sale is made) and
the estate agent's estimated probability of making a sale are given below:
1. Draw up an appropriate decision tree for the estate agent.
2. What is the estate agent's best strategy under Expected monitory value approach
(EMV)?
07
OR
Q.5 (a) Describe the steps involved in process of decision making. What are pay off and
regret functions? How can entries in regret table be derived from pay off table?
03
(b) Find the sequence that minimizes the total time required in performing the following
jobs on three machines in order ABC. Processing times (in hours) are given in the
following table:
Job 1 2 3 4 5
Machine A 8 10 6 7 11
Machine B 5 6 2 3 4
Machine C 4 9 8 6 5
04
(c) The following mortality rates have been observed for a certain type of fuse:
Week 1 2 3 4 5
Percentage failing by
the end of week
5 15 35 57 100
There are 1000 fuses in use and it costs Rs. 5 to replace an individual fuse. If all
fuses were replaced simultaneously it would cost Rs. 1.25 per fuse. It is proposed
to replace all fuses at fixed intervals of time, whether or not they have burnt out,
and to continue replacing burnt out fuses they fail. At what time intervals should the
group replacement be made? Also prove that this optimal policy is superior to the
straight forward policy of replacing each fuse only when it fails.
07
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This post was last modified on 20 February 2020