Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 6th Sem Old 161601 Modelling Simulation And Operations Research Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (OLD) EXAMINATION ? WINTER 2018
Subject Code:161601 Date: 15/12/2018
Subject Name: Modelling Simulation And Operations Research
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) State the definition of Operation Research. Also explain the applications of Operation Research. 07
(b) A manufacturer produces two types of models M1 and M2. Each model of the type M1 requires 4
hours of grinding and 2 hours of polishing; whereas each model of M2 requires 2 hours of grinding
and 5 hours of polishing. The manufacturer has 2 grinders and 3 polishers. Each grinder works for
40 hours a week and each polisher works 60 hours a week. Profit on M1 model is Rs.3.00 and on
model M2 is Rs.4.00. Whatever produced in a week is sold in the market. How should the
manufacturer allocate his production capacity to the two types of models, so that he makes
maximum profit in a week?
07
Q.2 (a) Solve the following LPP by graphical method
Maximize Z = 5X1 + 3X2 Subject to constraints
2X1 + X2 ? 1000
X1 ? 400
X1 ? 700 where X1, X2 ? 0
07
(b) Solve following LPP using Simplex Method:
5X
1
+ 10X
2
+ 8X
3
= Z (Z is the total profit per day) which is to be maximized
Constraints 3X
1
+ 4X
2
+5X
3
? 60
5X
1
+ 4X
2
+4X
3
? 72
2X
1
+ 4X
2
+5X
3
? 100
X
1
, X
2
, X
3
? 0??????..Non negativity constraint
OR
(b) Solve following LPP by Big-M method.
60X1 + 80X2 = G (G is the total cost per day which is to be minimized)
Constraints:20X
1
+30X
2
? 900
40X
1
+30X
2
? 1200
X
1
, X
2
? 0??????Non-negativity constraint
07
Q.3 (a) Explain primal and dual relationship. 07
(b) Solve blow example using North West Corner rule, the Least Cost method and the Vogel?s
Approximation Method of obtaining an initial feasible solution for a transportation problem.
07
OR
Q.3 (a) A company has three production facilities S
1
, S
2
and S
3
with production capacity of 7, 9 and 18
units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses
D
1
, D
2
, D
3
and D
4 with
requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively.
The transportation costs (in rupees) per unit between factories to warehouses are given in the table
below.
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (OLD) EXAMINATION ? WINTER 2018
Subject Code:161601 Date: 15/12/2018
Subject Name: Modelling Simulation And Operations Research
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) State the definition of Operation Research. Also explain the applications of Operation Research. 07
(b) A manufacturer produces two types of models M1 and M2. Each model of the type M1 requires 4
hours of grinding and 2 hours of polishing; whereas each model of M2 requires 2 hours of grinding
and 5 hours of polishing. The manufacturer has 2 grinders and 3 polishers. Each grinder works for
40 hours a week and each polisher works 60 hours a week. Profit on M1 model is Rs.3.00 and on
model M2 is Rs.4.00. Whatever produced in a week is sold in the market. How should the
manufacturer allocate his production capacity to the two types of models, so that he makes
maximum profit in a week?
07
Q.2 (a) Solve the following LPP by graphical method
Maximize Z = 5X1 + 3X2 Subject to constraints
2X1 + X2 ? 1000
X1 ? 400
X1 ? 700 where X1, X2 ? 0
07
(b) Solve following LPP using Simplex Method:
5X
1
+ 10X
2
+ 8X
3
= Z (Z is the total profit per day) which is to be maximized
Constraints 3X
1
+ 4X
2
+5X
3
? 60
5X
1
+ 4X
2
+4X
3
? 72
2X
1
+ 4X
2
+5X
3
? 100
X
1
, X
2
, X
3
? 0??????..Non negativity constraint
OR
(b) Solve following LPP by Big-M method.
60X1 + 80X2 = G (G is the total cost per day which is to be minimized)
Constraints:20X
1
+30X
2
? 900
40X
1
+30X
2
? 1200
X
1
, X
2
? 0??????Non-negativity constraint
07
Q.3 (a) Explain primal and dual relationship. 07
(b) Solve blow example using North West Corner rule, the Least Cost method and the Vogel?s
Approximation Method of obtaining an initial feasible solution for a transportation problem.
07
OR
Q.3 (a) A company has three production facilities S
1
, S
2
and S
3
with production capacity of 7, 9 and 18
units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses
D
1
, D
2
, D
3
and D
4 with
requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively.
The transportation costs (in rupees) per unit between factories to warehouses are given in the table
below.
07
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2
D
1
D
2
D
3
D
4
Capacity
S
1
19 30 50 10 7
S
2
70 30 40 60 9
S
3
40 8 70 20 18
Demand 5 8 7 14 34
Formulate this transportation problem as an LP model to minimize the total transportation cost.
(b) Consider the following transportation cost table. The costs are given in Rupees, the supply and
demand are in units. Determine an optimal solution.
07
Q.4 (a) Explain HAM method in detail 07
(b) Draw a network
Activity Immediate Predecessor(s) Activity Immediate Predecessor(s)
A - H F
B - I C,D,G,H
C - J I
D - K I
E A L J,K
F B M J,K
G E N M
07
OR
Q.4 (a) Solve the assignment optimal solution using HAM.
Time Taken (in minutes) by 4 worker
Worker
Job
A B C D
1 45 40 51 67
2 57 42 63 55
3 49 52 48 64
4 41 45 60 55
07
(b) Given the following information on a small project: A is the first activity of the project and precedes
the activity B and C. The activity D succeeds both B and C whereas only C is required to start
activity E. D precedes F while G succeeds E. H is the last activity of the project and succeeds F and
G. Draw a network based on this information.
07
Q.5 (a) What is queuing theory? Explain operating characteristics of the queuing system. 07
(b) What is Replacement? Explain Group and individual replacement policies giving by example. 07
OR
Q.5 (a) A confectioner sells confectionery items past data of demand per week in 100 kg with frequency
is given below.
Demand per week 0 5 10 15 20 25
Frequency 2 11 8 21 5 3
Using the following sequence of random number generate the demand for next 15 weeks, also
find average demand per week Random : 35,52,90,13,23,73,34,57,83,94,56,67,66,60
07
(b) A TV repairman finds that the time spent on his job has an exponential distribution with mean 30
minutes. If he repairs set in the order in which they come and if the arrival of sets is approximately
Poisson with an average rate of 10 per 8-hour day, what is his expected idle time each day? How
many jobs are ahead of the set just brought in?
07
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This post was last modified on 20 February 2020