b.tech.[sem vii (ce, me, it, ei, en, cs & ec – all groups...

EOE-073/ Mr. Puneet Sharma, .Dr. S. B. Tiwari & Dr. J. P. Ojha. Date: 08/ 09/2014

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SHRIRAMSWAROOPMEMORIALCOLLEGEOFENGG.&MANAGEMENT

B.Tech.[SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1

(Session: 2014-15)

OPERATIONS RESEARCH (EOE-073)

Roll No.

(To be filled by the Student) Note: Attempt all questions

Part – A (Questions from Tutorial Sheet)

[10 Marks]

1) A toy company manufactures two types of doll; a basic version – doll A and a deluxe version – doll B.

Each doll of type B, takes twice as long to produce as one of type A, and the company would have time

to make a maximum of 2000 per day if it produced only the basic version. The supply of plastic is

sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy

dress of which there are 600 per day available. If the company makes profit of Rs. 3.00 and Rs. 5.00, per

doll respectively on doll A and B; how many of each should be produced per day in order to maximize

profit? (Q. No. 4) [05]

2) Write the dual of the following LPP: (Q. No. 6-ii) [05]

.,0;10;82;224. 2121212121 signinedunrestrictxxxxxxxxtosubjectxxzMax ≥≤−=+≥−+=

Part – B [20 Marks]

3) What are the essential features of operations research? Mention different phases in an operations

research study. [03+03] 4) Solve graphically to the following linear programming problem. [06]

0,;60;80;200,83. ≥≥≤=++= yxyxyxtosubjectyxZMin

5) Solve the following LPP: [08]

;2052;153232 3213214321 =++=++−++= xxxxxxtosubjectxxxxZMax

0,,,102 43214321 ≥=+++ xxxxandxxxx

__________X__________

Academic/26 Refer/WI/ACAD/18

Time:1 Hour Max. Marks: 30


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SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT

B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1

(Session: 2014-15)


Roll No.



[10 Marks]

1) Define O.R. and discuss its characteristics and shortcomings. (Q. No. 2) [01+03]

2) Use dual simplex method to solve the following LPP [06]

0,1;22 21212121 ≥≥−−≥++= xxandxxxxtosubjectxxzMin (Q. No. 10)


3) Write short note on the following [2×3=06]

(i) Feasible and Infeasible solution (ii) Optimal and unbounded solution (iii) Degenerate and non-degenerate solution.

4) Solve graphically to the following linear programming problem. [06]




0,,,102 43214321 ≥=+++ xxxxandxxxx .

__________X__________


Time: 1 Hour Max. Marks: 30


Page-1



(Session: 2014-15)


Roll No.



[10 Marks]

1) Define Operations Research? Throw light on the growing importance of O.R. in business decisions.

(Q. No. 1) [02+02]

2) Solve by graphical method the following linear programming problem.

0,;4;8;2;122321. 21212112121 ≥≥+−≥+≤≤+⎟⎠⎞

⎜⎝⎛+= xxandxxxxxxxtosubjectxxzMax

(Q. No.5-ii) [06]


3) Write short note on the following [2×3=06]

(i) Feasible and Infeasible solution (ii) Optimal and unbounded solution (iii) Degenerate and non-degenerate solution.

4) Obtain the dual of the following primal problem: [06] Min Z = 3x1 - 2x2 + x3 s.t. 2x1 - 3x2 + x3 ≤ 5; 4x1 - 2x2 ≥ 9; -8x1 + 4x2 + 3x3 = 8; x1, x2 ≥ 0.



0,,,102 43214321 ≥=+++ xxxxandxxxx

__________X__________




Page-1


B.Tech.[SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1

(Session: 2014-15)


Roll No.



[10 Marks]

1) Solve graphically the following linear programming problem. [05]

0,2,4;1232;22;124353.

21

2121212121

≥≥≤≥+−≥−≤+−+=

xxandxxxxxxxxtosubjectxxzMin

(Q. No. 3-ii)

2) Solve the given LPP using Simplex method. [05]

0,,10834;1242;72323

321

32121321321

≥≤++−≤+−≤+−+−=

xxxandxxxxxxxxtosubjectxxxzMin

(Q. No. 8)

Part – B

[20 Marks]


research study. [03+03] 4) Obtain the dual of the following primal problem: [06]

Min Z = 3x1 - 2x2 + x3 s.t. 2x1 - 3x2 + x3 ≤ 5; 4x1 - 2x2 ≥ 9; -8x1 + 4x2 + 3x3 = 8; x1, x2 ≥ 0.



0,,,102 43214321 ≥=+++ xxxxandxxxx

__________X__________




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(Session: 2014-15)


Roll No.



[10 Marks]

1) Define slack and surplus variables with example used in LPP. (Q. No. 5-i) [03]

2) Use Big-M method to solve the problem: [07]

Minimize 21 32/15 xxz −= s. t. 33 321 ≥−− xxx ; 2321 ≥+− xxx and 0,, 321 ≥xxx . (Q. No.12)



research study. [03+03] 4) Solve graphically to the following linear programming problem. [06]




0,,,102 43214321 ≥=+++ xxxxandxxxx

__________X__________



EOE-073/Mr.Puneet Sharma, .Dr. S. B. Tiwari&Dr. J. P. Ojha. Date: 13/10/2014

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B.Tech.[SEM VII (CE, ME, IT, EI, EN, CS, EE& EC – All Groups)] QUIZ TEST-2

(Session: 2014-15)


Roll No.



[10 Marks]

1) We have five jobs, each of which must go through the machines A, B and C in the order ABC. Determine the sequence that will minimize the total elapsed time. [10]

Job No.→ 1 2 3 4 5 Machine A 5 7 6 9 5 Machine B 2 1 4 5 3 Machine C 3 7 5 6 7

(T2 Q. No. 12)


2) Find optimal solution to the following transportation problem. [07]

Origins Destinations Supply I II III A 2 7 4 5 B 3 3 1 8 C 5 4 7 7 D 1 6 2 14

Demand 7 9 18

3) Solve the following assignment problem. [07]


I II III IV V VI A 9 22 58 11 19 27 B 43 78 72 50 63 48 C 41 28 91 37 45 33 D 74 42 27 49 39 32 E 36 11 57 22 25 18 F 3 56 53 31 17 28


P. T.O.

EOE-073/Mr.Puneet Sharma, .Dr. S. B. Tiwari&Dr. J. P. Ojha. Date: 13/10/2014

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4) Determine the optimal sequence of jobs that minimizes the total elapsed time based on the following information processing time on machines is given in hours and passing is not allowed. Also, find idle times for each machine. [06]

Job No. A B C D E F G Machine M1 3 8 7 4 9 8 7 Machine M2 4 3 2 5 1 4 3 Machine M3 6 7 5 11 5 6 12

__________X__________

EOE-073/Mr.Puneet Sharma, .Dr. S. B. Tiwari& Dr. J. P. Ojha. Date: 13/10/2014

Page-1


B.Tech.[SEM VII (CE, ME, IT, EI, EN, CS, EE & EC – All Groups)] QUIZ TEST-2

(Session: 2014-15)


Roll No.



[10 Marks]

1) Consider the following transportation problem [10]

It is not possible to transport any quantity from factory B to Godown V. Determine: (i) Initial solution by Vogel’s Approximation method.

(ii) Optimum basic feasible solution. (iii) Is the optimum solution unique? If not, find the alternative

optimum basic feasible solution.( T2 Q. No. 3)




Demand 7 9 18


Factory Godowns Stock Available I II III IV V VI

A 7 5 7 7 5 3 60 B 9 11 6 11 ─ 5 20 C 11 10 6 2 2 8 90 D 9 10 9 6 9 12 50 Demand 60 20 40 20 40 40


P. T.O.


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Job No. A B C D E F G

Machine M1 3 8 7 4 9 8 7 Machine M2 4 3 2 5 1 4 3 Machine M3 6 7 5 11 5 6 12

__________X__________



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SHRI RAMSWAROOP MEMORIAL COLLEGE OFENGG.&MANAGEMENT


(Session: 2014-15)


Roll No.



[10 Marks]

1) A college department chairman has the problem of providing teachers for all courses offered by hisdepartment at the highest possible level of educational 'quality'. He has one professor, two associate professors, and one teaching assistant (TA) available. Four courses must be offered and, after appropriate introspection and evaluation he has arrived at the following relative ratings (100 = basic rating) regarding the ability of each instructor to teach the four courses, respectively. [10]

Courses 1 2 3 4

Prof. 1 60 40 60 70 Prof. 2 20 60 50 70 Prof. 3 20 30 40 60 T.A. 30 10 30 40 (T2 Q. No. 9)

How should he assign his staff to the courses to maximize educational quality in his department?




Demand 7 9 18



P. T.O.


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__________X__________



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(Session: 2014-15)


Roll No.



[10 Marks]

1) Solve the following transportation problem to maximize profit and give criteria for optimality. [10]

Origins Profit (Rs.)/Unit. Destinations Supply

I II III IV A 40 25 22 33 100 B 44 35 30 30 30 C 38 38 28 30 70

Demands 40 20 60 30 (T2 Q. No. 5)

Part – B

[20 Marks]



Demand 7 9 18





P. T.O.


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__________X__________


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(Session: 2014-15)


Roll No.



[10 Marks]

1) There are 5 jobs to be assigned, one each to 5 persons and the profit for each person on each job is given

as: [10]

Persons

Jobs

Find the optimal assignment to maximize the profit. (T2 Q. No. 7)




Demand 7 9 18


A B C D E I 11 17 8 16 20 II 9 7 12 6 15 III 13 16 15 12 16 IV 21 24 17 28 26 V 14 10 12 11 15


P. T.O.


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__________X__________


EOE-073 / Dr. Puneet Sharma, .Dr. S. B. Tiwari&Dr. J. P. Ojha. Date: 17/11/2014

Page-1


B.Tech.[SEM VII (CE, ME, IT, EI, EN, CS, EE& EC – All Groups)] QUIZ TEST-03

(Session: 2014-15)


Roll No.



[10 Marks]

1) A project has the following characteristics: [05]

Activity Preceding activity Expected completion time A None 5 B A 2 C A 6 D B 12 E D 10 F D 9 G D 5 H B 9 I C, E 1 J G 2 K F, I, J 3 L K 9 M H, G 7 N M 8

i) Draw a PERT network for this project. ii) Find the critical path and project completion time. iii) Compute EST, EFT, LST, LFT. (T3 Q. No. 4)

2) Consider a “modified” form of “matching biased coins” game problem. The matching player is paid Rs. 8.00 if the two coins turn both heads and Rs.1.00 if the coins turn both tails. The non-matching player is paid Rs.3.00 when the two coins do not match. Given the choice of being the matching or non-matching player, which one would you choose and what would be your strategy? (T4 Q. No. 6) [05]



P. T.O.

EOE-073 / Dr. Puneet Sharma, .Dr. S. B. Tiwari&Dr. J. P. Ojha. Date: 17/11/2014

Page-2


3) What is project management? Explain the phases of project management. [2+4]

4) Solve the following game. [06]

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

212673175117132646418

4321

A Player

BPlayer IVIIIIII

5) Listed in the table are the activities and sequencing requirements necessary for the completion of a

research project. [08]

i) Draw a network diagram for this project.

ii) Find the critical path and duration of the project.

iii) Find the total float for each activity.

__________X__________

Activity Description Predecessor Duration (week)

A Literature search - 6

B Formulation of hypothesis - 5

C Preliminary feasibility study B 2

D Formal disposal C 2

E Field analysis A, D 2

F Progress report D 1

G Formal research A, D 6

H Data collection E 5

I Data analysis G, H 6

J Conclusions I 2

K Rough draft G 4

L Final copy J, K 3

M Preparation of oral presentation L 1

EOE-073/ Dr. Puneet Sharma, .Dr. S. B. Tiwari& Dr. J. P. Ojha. Date: 17/11/2014

Page-1



(Session: 2014-15)


Roll No.



[10 Marks]

1) A project has the following time schedule: [05]

Activity: 1-2 1-3 1-4 2-5 3-6 3-7 4-6 5-8 6-9 7-8 8-9 Duration: 2 2 1 4 8 5 3 1 5 4 3

(in months) Construct PERT network and compute (i) Total float, free float and independent float for each activity,

(ii) Critical path and its duration. (T3 Q. No. 9)

2) In a game of matching coins with two players, suppose A wins one unit of value, when there are two

heads, wins nothing when there are two tails and losses 21 units of value when there are one head and

one tail. Determine the payoff matrix, the best strategies for each player and the value of the game to A.

(T4 Q. No. 3) [05]




⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

212673175117132646418

4321

A Player

BPlayer IVIIIIII



P. T.O.


Page-2






__________X__________











J Conclusions I 2

K Rough draft G 4

L Final copy J, K 3



Page-1

SHRI RAMSWAROOP MEMORIAL COLLEGE OFENGG.&MANAGEMENT


(Session: 2014-15)


Roll No.



[10 Marks]

1) The following table lists the jobs of a network with their time estimates. [05]

Job Duration(Days) i - j Optimistic Most likely Pessimistic 1 2 3 6 15 1 6 2 5 14 2 3 6 12 30 2 4 2 5 8 3 5 5 11 17 4 5 3 6 15 6 7 3 9 27 5 8 1 4 7 7 8 4 19 28

(a) Draw the project network. (b) Calculate the length and variance of the critical path. (c) What the is approximate probability that the jobs on the critical path will be completed by the due date of 4days? (d) What due date has about 90% chance of being met? (T3 Q. No. 6)

2) Solve the following games graphically. [05]

Player B

Player A

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−−

1234976521

(T4 Q. No. 5-ii)



P. T. O.


Page-2




⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

212673175117132646418

4321

A Player

BPlayer IVIIIIII






__________X__________











J Conclusions I 2

K Rough draft G 4

L Final copy J, K 3


EOE-073/ Dr .Puneet Sharma, .Dr. S. B. Tiwari& Dr. J. P. Ojha. Date: 17/11/2014

Page-1



(Session: 2014-15)


Roll No.



[10 Marks]

1) The utility data for a network are given below. Determine the total, free, independent and interfering

floats. Identify the critical path and project duration. (T3 Q. No. 8) [05]

Activity 0-1 1-2 1-3 2-4 2-5 3-4 3-6 4-7 5-7 6-7 Duration 2 8 10 6 3 3 7 5 2 8

2) A and B play game in which each has three coins, a 5p, 10p and a 20p. Each selects a coin without the

knowledge of the other’s choice. If the sum of the coins is an odd amounts, A wins B’s coin, if the sum

is even, B wins A’s coin. Find the best strategy for each player and the value of the game. (T4 Q. No. 4)

[05]

Part – B

[20 Marks]



⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

212673175117132646418

4321

A Player

BPlayer IVIIIIII



P. T.O.

EOE-073/ Dr .Puneet Sharma, .Dr. S. B. Tiwari& Dr. J. P. Ojha. Date: 17/11/2014

Page-2






__________X__________











J Conclusions I 2

K Rough draft G 4

L Final copy J, K 3



Page-1



(Session: 2014-15)


Roll No.



[10 Marks]

1) A small project is composed of 7 activities whose time estimates are listed in table below. Activities are identified by their beginning (i) and ending (j) node numbers [05]

Activity (i-j) 1-2 1-3 1-4 2-5 3-5 4-6 5-6 Optimistic time 1 1 2 1 2 2 3 Most likely time 1 4 2 1 5 5 6

Pessimistic time 7 7 8 1 14 8 15 (a) Draw the network diagram of activities in the project. (b) Find the expected duration and variance for each activity. (c) Identify the critical path. (T3 Q. No.5)

2) Solve the following games graphically. [05] Player B

Player A ⎥⎦

⎤⎢⎣

⎡ −23012012

(T4 Q. No. 5-i)




⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

212673175117132646418

4321

A Player

BPlayer IVIIIIII



P. T.O.


Page-2






__________X__________











J Conclusions I 2

K Rough draft G 4

L Final copy J, K 3


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