Categories: 7th Semester

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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