GUJARAT TECHNOLOGICAL UNIVERSITY
SEMESTER-VI(OLD) - EXAMINATION - SUMMER 2019
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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:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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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 07 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 Platingm Gold required/unit Profit/unit (Rs)
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required/unit (gms) (gms)
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?
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Formulate it as a linear programing problem.
Q.2 (a) Solve the following LPP by graphical method 07
Minimize Z=40y1 + 242 Total Cost
Subject to
20x;+50x2>4800 Phosphate Requirement
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80x;+50x2>7200 Nitrogen Requirement
X1,X2>0
(b) Solve following LPP using Simplex Method: 07
Minimize Z=40x; + 35x2 Profit
Subject to
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2x1+3x,<60 Raw Material Constrain
4x;+3x,<96 Labor Hours Constrain
X1,X2 >0
OR
(b) Solve following LPP by Big-M method. 07
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Minimize Z=120x; + 60x2
Subject to
20x; +30x2>900
40x; +30x2 > 1200
X1,X2>0
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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 07 initial feasible solution for a transportation problem.
To= P R S Suppl
From{ Q PPy
A 12 10 12 13 500
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B 7 11 8 14 300
C 6 16 11 7 200
Demand 180 150 350 320 1000
OR
Q.3 (a) Explain primal and dual relationship. 07
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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
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Demand 180 150 350 320 1000
Q.4 (a) Solve the following assignment problem by (a) enumeration method and (b) Hungarian assignment method 07
Time (in minutes
Worker Job 1 Job 2 Job 3
A 4 2 7
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B 8 5 3
C 4 5 6
(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: 07
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. Patrol unit
Incident
I
I
II
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v 3 7
(a) Which patrol units should respond?
(b) What will be the average response time?
(b) Draw a network from the below given information and determine the critical path 07
Activity Immediate Predecessor(s) Activity Immediate Predecessor(s)
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A - G CF
B - H B
C - I EH
D AB J EH
E B K C,D,FJ
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F B L K
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. 07
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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.
(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 07
(1) The probability that an arrival finds that four persons are waiting for their turn ;
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(11) The average number of persons waiting and making telephone calls ; and
(111) The average length of the queue that is formed from time to time.
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