GTU BE 7th Semester 172503 Optimization Methods Summer 2018 Question Paper

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE ? 7 SEMESTER (Old)? ? EXAMINATION ? SUMMER 2018
Subject Code:172503 Date:03/05/2018
Subject Name: Optimization Methods
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 the process of developing OR Model 07
(b) What is graphical method of solving Linear Programming problem? Explain
with suitable example
07

Q.2 (a) Solve following problem with simplex method
Max Z=10x+15y+20z
Subject to 2x+4y+6z ? 24
3x+9y+6z ? 30
x,y,z ? 0
07
(b) Explain duality in linear programming problem with suitable example 07
OR
(b) A small manufacturer employs five skilled men and ten semi-skilled men for
making a product in two qualities: a deluxe model and an ordinary model. The
production of a deluxe model requires 2-hours work by a skilled man and a 2-hour
work by a semi-skilled man. The ordinary model requires 1-hour work by a skilled
man and a 3-hours work by a semi-skilled man. According to worker union?s rules,
no man can work more than 8-hours per day. The profit of the deluxe model is
Rs.1000 per unit and that of the ordinary model is Rs.800 per unit. Formulate a
linear programming model for this manufacturing situation to determine the
production volume of each model such that the total profit is maximized.
07

Q.3 (a)Solve following problem with Big M Method
Minimize Z=20x 1+10x 2
Subject to x 1+2x 2 ?40
3x 1+x 2=30
4x 1+3x 2 ?60
x 1,x 2 ?0
07
(b)Construct the dual of the problem:
Maximize Z = 3x+5y
Subject to x- 2y ? 3
x + 3y ?9
x ? y ? 5
x,y ? 0
07

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE ? 7 SEMESTER (Old)? ? EXAMINATION ? SUMMER 2018
Subject Code:172503 Date:03/05/2018
Subject Name: Optimization Methods
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 the process of developing OR Model 07
(b) What is graphical method of solving Linear Programming problem? Explain
with suitable example
07

Q.2 (a) Solve following problem with simplex method
Max Z=10x+15y+20z
Subject to 2x+4y+6z ? 24
3x+9y+6z ? 30
x,y,z ? 0
07
(b) Explain duality in linear programming problem with suitable example 07
OR
(b) A small manufacturer employs five skilled men and ten semi-skilled men for
making a product in two qualities: a deluxe model and an ordinary model. The
production of a deluxe model requires 2-hours work by a skilled man and a 2-hour
work by a semi-skilled man. The ordinary model requires 1-hour work by a skilled
man and a 3-hours work by a semi-skilled man. According to worker union?s rules,
no man can work more than 8-hours per day. The profit of the deluxe model is
Rs.1000 per unit and that of the ordinary model is Rs.800 per unit. Formulate a
linear programming model for this manufacturing situation to determine the
production volume of each model such that the total profit is maximized.
07

Q.3 (a)Solve following problem with Big M Method
Minimize Z=20x 1+10x 2
Subject to x 1+2x 2 ?40
3x 1+x 2=30
4x 1+3x 2 ?60
x 1,x 2 ?0
07
(b)Construct the dual of the problem:
Maximize Z = 3x+5y
Subject to x- 2y ? 3
x + 3y ?9
x ? y ? 5
x,y ? 0
07

2

OR
Q.3 (a)Find the initial basic feasible solution of the following transportation problem by
Vogel?s approximation method:
Warehouses
W 1 W 2 W 3 W 4 Capacity
F 1 10 30 50 10 7
F 2 70 30 40 60 9
F 3 40 8 70 20 18
Requirement 5 8 7 14 34
07
(b) Describe Transshipment problem with suitable example 07

Q.4 (a)Solve the following assignment problem using Hungerian method. The matrix entries
are processing times in hours.
Operator
1 2 3 4 5

1 20 22 35 22 18
2 4 26 24 24 7
Job 3 23 14 17 19 19
4 17 15 16 18 15
07
(b) Explain travelling sales-man problem with suitable example
07
OR
Q.4 (a)There is congestion on the platform of Ahmedabad Railway station. The trains arrive at
the rate of 30 trains per day. The waiting time for any train to flag-off is exponentially
distributed with an average of 36 minutes. Calculate the following:
i) The mean queue size.
ii) The probability that the queue size exceeds 10.
07
(b) Explain M/M/1 model of queuing in detail with suitable example 07

Q.5 (a) Solve following game problem

Player A
Player B
1 2 3 4
1 6 2 4 8
2 2 -1 1 12
3 2 3 3 9
4 5 2 6 10
07
(b) Explain method of Linear Programming to solve game problem with suitable
example
07
OR
Q.5 (a) Explain Inventory model of simulation with suitable example 07
(b) Describe advantages and dis-advantages of simulation in detail 07
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