Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 7th Sem New 21720042172011 Production Optimization Techniques Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2172004/2172011 Date: 29/11/2018
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.
Q.1 (a) ?Every Linear programming problem exists in pair? Evaluate. 03
(b) With reference to the graphical method, discuss (i) Feasibility of an Unbounded solution
space with an Optimum solution for a maximization problem (ii) Similarity and difference
between an unbounded and infeasible solution.
04
(c) Define the following
1. Redundant constraint 2. Slack Variable 3. Artificial variable
07
Q.2 (a) What do you understand by shadow price? What is the reason of selecting the minimum
value of bi / aij as the basis for an outgoing variable?
03
(b) Solve
Maximize Z = 2x ? 3y + z
Subject to
3x + 6y + z ? 6
4x + 2y + z ? 4
x ? y + z ? 3
and x ? 0, y ? 0, z ? 0
04
(c) A machine tool company conducts a job-training programme at a ratio of one for every ten
trainees. The training programme lasts for one month. From past experience it has been
found that out of 10 trainees hired, only seven complete the programme successfully. (The
unsuccessful trainees are released). Trained machinists are also needed for machining.
The company's requirement for the next three months is as follows:
January: 100 machinists, February: 150 machinists and March: 200 machinists.
In addition, the company requires 250 trained machinists by April. There are 130 trained
machinists available at the beginning of the year.
Pay roll cost per month is:
Each trainee Rs. 400/- per month.
Each trained machinist (machining or teaching): Rs. 700/- per month.
Each trained machinist who is idle: Rs.500/- per month.
(Labor union forbids ousting trained machinists). Build a LPP for producing the minimum
cost hiring and training schedule and meet the company?s requirement. Do not solve.
07
OR
(c) Solve : Maximize Z = 8x2
Subject to : x1 - x2 ? 0; 2x1 + 3x2 ? - 6; and x1 , x2 unrestricted
07
Q.3 (a) Explain the significance of sensitivity analysis in a LPP. 03
(b) Solve using two phase method
Min Z = x1 ? 2x2 ? 3x3
Subject to
? 2x1 + x2 + 3x3 = 2
2x1 + 3x2 + 4x3 = 1
and x1 ? 0, x2 ? 0 , x3 ? 0
04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2172004/2172011 Date: 29/11/2018
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.
Q.1 (a) ?Every Linear programming problem exists in pair? Evaluate. 03
(b) With reference to the graphical method, discuss (i) Feasibility of an Unbounded solution
space with an Optimum solution for a maximization problem (ii) Similarity and difference
between an unbounded and infeasible solution.
04
(c) Define the following
1. Redundant constraint 2. Slack Variable 3. Artificial variable
07
Q.2 (a) What do you understand by shadow price? What is the reason of selecting the minimum
value of bi / aij as the basis for an outgoing variable?
03
(b) Solve
Maximize Z = 2x ? 3y + z
Subject to
3x + 6y + z ? 6
4x + 2y + z ? 4
x ? y + z ? 3
and x ? 0, y ? 0, z ? 0
04
(c) A machine tool company conducts a job-training programme at a ratio of one for every ten
trainees. The training programme lasts for one month. From past experience it has been
found that out of 10 trainees hired, only seven complete the programme successfully. (The
unsuccessful trainees are released). Trained machinists are also needed for machining.
The company's requirement for the next three months is as follows:
January: 100 machinists, February: 150 machinists and March: 200 machinists.
In addition, the company requires 250 trained machinists by April. There are 130 trained
machinists available at the beginning of the year.
Pay roll cost per month is:
Each trainee Rs. 400/- per month.
Each trained machinist (machining or teaching): Rs. 700/- per month.
Each trained machinist who is idle: Rs.500/- per month.
(Labor union forbids ousting trained machinists). Build a LPP for producing the minimum
cost hiring and training schedule and meet the company?s requirement. Do not solve.
07
OR
(c) Solve : Maximize Z = 8x2
Subject to : x1 - x2 ? 0; 2x1 + 3x2 ? - 6; and x1 , x2 unrestricted
07
Q.3 (a) Explain the significance of sensitivity analysis in a LPP. 03
(b) Solve using two phase method
Min Z = x1 ? 2x2 ? 3x3
Subject to
? 2x1 + x2 + 3x3 = 2
2x1 + 3x2 + 4x3 = 1
and x1 ? 0, x2 ? 0 , x3 ? 0
04
2
(c) Explain the following related to simplex table:
(i) Degeneracy & cycling
(ii) Unbounded solution
(iii) Alternate multiple solution
07
OR
Q.3 (a) Compare and Contrast : Assignment and transportation problem 03
(b) Discuss the techniques for obtaining an optimum solution to a transportation problem. 04
(c) A company has three factories X, Y, and Z and four warehouses A, B, C, and D. It is
required to schedule factory production and shipments from factories to warehouses in
such a manner so as to minimize total cost of shipment and production. Unit variable
manufacturing costs (UVMC) and factory capacities and warehouse requirements are
given below:
Find the optimal production and transportation schedule
07
Q.4 (a) Explain merge and burst event. 03
(b) Discuss different types of floats in network analysis 04
(c) Explain the significance of Crashing and Resource allocation with a suitable example.
Explain the Johnsons rule of Sequencing with a suitable example.
07
OR
Q.4 (a) Explain the Kendalls notation to a queuing problem 03
(b) Discuss the types of inventories with suitable example. 04
(c) A company has 5 jobs to be done. The following matrix shows the return in terms of
rupees on assigning i
th
( i = 1, 2, 3, 4, 5 ) machine to the j
th
job ( j = A, B, C, D, E ).
Assign the five jobs to the five machines so as to maximize the total expected profit.
07
Q.5 (a) Explain Dangling and Looping. Why they should be avoided? 03
(b) Discuss: EOQ, Price-break, Lead-time, Buffer stock. 04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2172004/2172011 Date: 29/11/2018
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.
Q.1 (a) ?Every Linear programming problem exists in pair? Evaluate. 03
(b) With reference to the graphical method, discuss (i) Feasibility of an Unbounded solution
space with an Optimum solution for a maximization problem (ii) Similarity and difference
between an unbounded and infeasible solution.
04
(c) Define the following
1. Redundant constraint 2. Slack Variable 3. Artificial variable
07
Q.2 (a) What do you understand by shadow price? What is the reason of selecting the minimum
value of bi / aij as the basis for an outgoing variable?
03
(b) Solve
Maximize Z = 2x ? 3y + z
Subject to
3x + 6y + z ? 6
4x + 2y + z ? 4
x ? y + z ? 3
and x ? 0, y ? 0, z ? 0
04
(c) A machine tool company conducts a job-training programme at a ratio of one for every ten
trainees. The training programme lasts for one month. From past experience it has been
found that out of 10 trainees hired, only seven complete the programme successfully. (The
unsuccessful trainees are released). Trained machinists are also needed for machining.
The company's requirement for the next three months is as follows:
January: 100 machinists, February: 150 machinists and March: 200 machinists.
In addition, the company requires 250 trained machinists by April. There are 130 trained
machinists available at the beginning of the year.
Pay roll cost per month is:
Each trainee Rs. 400/- per month.
Each trained machinist (machining or teaching): Rs. 700/- per month.
Each trained machinist who is idle: Rs.500/- per month.
(Labor union forbids ousting trained machinists). Build a LPP for producing the minimum
cost hiring and training schedule and meet the company?s requirement. Do not solve.
07
OR
(c) Solve : Maximize Z = 8x2
Subject to : x1 - x2 ? 0; 2x1 + 3x2 ? - 6; and x1 , x2 unrestricted
07
Q.3 (a) Explain the significance of sensitivity analysis in a LPP. 03
(b) Solve using two phase method
Min Z = x1 ? 2x2 ? 3x3
Subject to
? 2x1 + x2 + 3x3 = 2
2x1 + 3x2 + 4x3 = 1
and x1 ? 0, x2 ? 0 , x3 ? 0
04
2
(c) Explain the following related to simplex table:
(i) Degeneracy & cycling
(ii) Unbounded solution
(iii) Alternate multiple solution
07
OR
Q.3 (a) Compare and Contrast : Assignment and transportation problem 03
(b) Discuss the techniques for obtaining an optimum solution to a transportation problem. 04
(c) A company has three factories X, Y, and Z and four warehouses A, B, C, and D. It is
required to schedule factory production and shipments from factories to warehouses in
such a manner so as to minimize total cost of shipment and production. Unit variable
manufacturing costs (UVMC) and factory capacities and warehouse requirements are
given below:
Find the optimal production and transportation schedule
07
Q.4 (a) Explain merge and burst event. 03
(b) Discuss different types of floats in network analysis 04
(c) Explain the significance of Crashing and Resource allocation with a suitable example.
Explain the Johnsons rule of Sequencing with a suitable example.
07
OR
Q.4 (a) Explain the Kendalls notation to a queuing problem 03
(b) Discuss the types of inventories with suitable example. 04
(c) A company has 5 jobs to be done. The following matrix shows the return in terms of
rupees on assigning i
th
( i = 1, 2, 3, 4, 5 ) machine to the j
th
job ( j = A, B, C, D, E ).
Assign the five jobs to the five machines so as to maximize the total expected profit.
07
Q.5 (a) Explain Dangling and Looping. Why they should be avoided? 03
(b) Discuss: EOQ, Price-break, Lead-time, Buffer stock. 04
3
(c) The following matrix gives the payoff of different strategies (alternatives) A, B, and C
against conditions (events) W, X, Y and Z. Identify the decision taken under the following
approaches: (i) Pessimistic, (ii) Optimistic, (iii) Equal probability, (iv) Regret, (v)
Hurwicz criterion. The decision maker?s degree of optimism (?) being 0.7.
07
OR
Q.5 (a) Differentiate between Decision node and Chance node. 03
(b) Explain: Decision making under risk & under uncertainty. 04
(c) A fleet owner finds form his past records that the cost per year of running a vehicle whose
purchase price is Rs. 50000/- are as under:
Thereafter running cost increases by Rs.2000/- per year but resale value remains constant
at Rs. 2000/-. At what stage the replacement is due?
07
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This post was last modified on 20 February 2020