Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 6th Sem Old 161601 Modelling Simulation And Operations Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(OLD) ? EXAMINATION ? SUMMER 2019
Subject Code:161601 Date:29/05/2019
Subject Name: Modelling Simulation And Operations 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) State the definition of Operation Research. Also explain the phases of Operation Research. 07
(b) What is LPP? A company manufacturer 3 types of pats which use precious metals platinum and
gold. Due to shortage of these precious metals, the government regulates the amount that may be
used per day. The relevant data with respect to supply, requirements, and profits are summarized in
the table as follows:
Product
Platinum
required/unit (gms)
Gold required/unit
(gms)
Profit/unit (Rs)
A 2 3 500
B 4 2 600
C 6 4 1200
Daily allotment of platinum and gold are 160gm and 120gm respectively. How should the company
divided the supply of scarce precious metals?
Formulate it as a linear programing problem.
07
Q.2 (a) Solve the following LPP by graphical method
Minimize Z=40 x1 + 24 x2 Total Cost
Subject to
20 x 1 + 50 x 2 > 4800 Phosphate Requirement
80 x 1 + 50 x 2 > 7200 Nitrogen Requirement
x 1, x 2 > 0
07
(b) Solve following LPP using Simplex Method:
Minimize Z=40x 1 + 35x 2 Profit
Subject to
2 x 1 + 3 x 2 < 60 Raw Material Constrain
4 x 1 + 3 x 2 < 96 Labor Hours Constrain
x 1, x 2 > 0
07
OR
(b) Solve following LPP by Big-M method.
Minimize Z=120x 1 + 60x 2
Subject to
20 x 1 + 30 x 2 > 900
40 x 1 + 30 x 2 > 1200
x 1, x 2 > 0
07
Q.3 (a) Formulate classical transportation problem mathematically or provide transportation model 07
(b) Solve below example using North West Corner rule and the Least Cost method of obtaining an
initial feasible solution for a transportation problem.
From
To
P Q R S Supply
A 12 10 12 13 500
B 7 11 8 14 300
C 6 16 11 7 200
Demand 180 150 350 320 1000
07
OR
Q.3 (a) Explain primal and dual relationship.
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(OLD) ? EXAMINATION ? SUMMER 2019
Subject Code:161601 Date:29/05/2019
Subject Name: Modelling Simulation And Operations 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) State the definition of Operation Research. Also explain the phases of Operation Research. 07
(b) What is LPP? A company manufacturer 3 types of pats which use precious metals platinum and
gold. Due to shortage of these precious metals, the government regulates the amount that may be
used per day. The relevant data with respect to supply, requirements, and profits are summarized in
the table as follows:
Product
Platinum
required/unit (gms)
Gold required/unit
(gms)
Profit/unit (Rs)
A 2 3 500
B 4 2 600
C 6 4 1200
Daily allotment of platinum and gold are 160gm and 120gm respectively. How should the company
divided the supply of scarce precious metals?
Formulate it as a linear programing problem.
07
Q.2 (a) Solve the following LPP by graphical method
Minimize Z=40 x1 + 24 x2 Total Cost
Subject to
20 x 1 + 50 x 2 > 4800 Phosphate Requirement
80 x 1 + 50 x 2 > 7200 Nitrogen Requirement
x 1, x 2 > 0
07
(b) Solve following LPP using Simplex Method:
Minimize Z=40x 1 + 35x 2 Profit
Subject to
2 x 1 + 3 x 2 < 60 Raw Material Constrain
4 x 1 + 3 x 2 < 96 Labor Hours Constrain
x 1, x 2 > 0
07
OR
(b) Solve following LPP by Big-M method.
Minimize Z=120x 1 + 60x 2
Subject to
20 x 1 + 30 x 2 > 900
40 x 1 + 30 x 2 > 1200
x 1, x 2 > 0
07
Q.3 (a) Formulate classical transportation problem mathematically or provide transportation model 07
(b) Solve below example using North West Corner rule and the Least Cost method of obtaining an
initial feasible solution for a transportation problem.
From
To
P Q R S Supply
A 12 10 12 13 500
B 7 11 8 14 300
C 6 16 11 7 200
Demand 180 150 350 320 1000
07
OR
Q.3 (a) Explain primal and dual relationship.
07
2
(b) Consider the following transportation problem. Obtain an initial feasible solution for a
transportation problem by VAM method.
From
To
P Q R S Supply
A 12 10 12 13 500
B 7 11 8 14 300
C 6 16 11 7 200
Demand 180 150 350 320 1000
07
Q.4 (a) Solve the following assignment problem by (a) enumeration method and (b) Hungarian
assignment method
Time (in minutes)
Worker Job 1 Job 2 Job 3
A 4 2 7
B 8 5 3
C 4 5 6
07
(b) Explain the difference between PERT and CPM 07
OR
Q.4 (a) A dispatcher of the police department has received four requests for police assistance. Currently
six patrol cars are available for assignment and the estimated response time (in minutes) are show
in the table that follows:
Incident
Patrol unit
1 2 3 4 5 6
I 6 5 3 4 5 6
II 8 6 2 3 7 6
II 4 4 7 6 5 5
IV 3 7 9 8 4 7
(a) Which patrol units should respond?
(b) What will be the average response time?
07
(b) Draw a network from the below given information and determine the critical path
Activity Immediate Predecessor(s) Activity Immediate Predecessor(s)
A - G C,F
B - H B
C - I E,H
D A,B J E,H
E B K C,D,F,J
F B L K
07
Q.5 (a) What is queuing theory? Explain general structure of the queuing system. 07
(b) What is simulation? Explain advantages, disadvantages and application of simulation. 07
OR
Q.5 (a) A firm is using a machine whose purchase price is Rs. 13000. The installation charges amount Rs.
3600 and the machine has a scrap value of Rs. 1600 because the firm has a monopoly of this type
of work. The maintenance cost in various years is given in the following table.
Year 1 2 3 4 5 6 7 8 9
Cost (Rs.) 250 750 1000 1500 2100 2900 4000 4800 6000
The firm wants to determine after how many years should the machine be replaced on economic
consideration assuming that the machine replacement can be done only at the year ends.
07
(b) Arrivals at the telephone booth are considered to be Poisson with an average time of 10minutes
between one arrival and the next. The length of a phone call is assumed to be distributed
exponentially with mean 3 minutes. Find
(i) The probability that an arrival finds that four persons are waiting for their turn ;
(ii) The average number of persons waiting and making telephone calls ; and
(iii) The average length of the queue that is formed from time to time.
07
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This post was last modified on 20 February 2020