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EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 10 / 09 / 2012
Page-1
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1
(Session: 2012-13)
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 manufacture of wooden articles produces tables and chairs which requires two types of inputs mainly,
these being wood and labour. The manufacturer knows that for a table 3 units of wood and 1 unit of
labour are required while for chair these are 2 units and 2 units respectively. The profit from each table
is Rs.20 while it is Rs.16 for each chair. The total available resources for the manufacturer are 150 units
of wood and 75 units of labour. The manufacturer wants to maximize his profit by distributing his
resources for tables and chairs. Formulate this as a linear programming problem. (Q. No. 3-i) [04]
2) Use two-phase simplex method to solve the problem:
Minimize 21 32
15 xxZ −= s. t. 33 321 ≥−− xxx ; 2321 ≥+− xxx and 0,, 321 ≥xxx . (Q. No. 8) [06]
Part – B [20 Marks]
3) Use Simplex method to solve: [08]
Max. Z = 2x1 + x2 subject to x1 - x2 ≤ 10; 2x1 – x2 ≤ 40; x1, x2 ≥ 0.
4) Solve the following linear programming problem graphically: [06]
Min. 21 25 xxZ −= s. t. 132 21 ≥+ xx ; 0, 21 ≥xx .
5) What is operations research? Explain general method for solving operations research models. [02+04]
__________X__________
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 10 / 09 / 2012
Page-1
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1
(Session: 2012-13)
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) Define Operations Research? Throw light on the growing importance of O.R. in business decisions.
(Q. No. 1) [02+02]
2) Use Simplex method to solve:
Max. Z = 3x1 + 5x2 + 4x3 Subject to 2x1 + 3x2 ≤8; 2x2 + 5x3 ≤ 10; 3x1 + 2x2 + 4x3 ≤ 15 and x1, x2, x3 ≥ 0.
(Q. No.6) [06] Part – B
[20 Marks]
3) Solve the following linear programming problem: [08]
Min Z = x1 - 2x2 - 3x3 subject to -2x1 + x2 + 3x3 = 2; 2x1 + 3x2 + 4x3 = 1 and x1, x2, x3 ≥ 0.
4) Solve the following linear programming problem graphically: [06]
Min. 21 25 xxZ −= s. t. 132 21 ≥+ xx ; 0, 21 ≥xx .
5) 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. Formulate this problem as LPP in order to maximize the profit? [06]
__________X__________
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 10 / 09 / 2012
Page-1
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1
(Session: 2012-13)
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) Define O.R. and discuss its characteristics and shortcomings. (Q. No. 2) [02+02]
2) Use Big-M method to maximize: 213 xxz −= s. t. 22 21 ≥+ xx ; 33 21 ≤+ xx ; 42 ≤x and 0, 21 ≥xx .
(Q. No.7) [06]
Part – B
[20 Marks]
3) Use Simplex method to solve: [08]
Max. Z = 2x1 + x2 subject to x1 - x2 ≤ 10; 2x1 – x2 ≤ 40; x1, x2 ≥ 0.
4) Solve the following linear programming problem graphically: [06]
Min. 21 25 xxZ −= s. t. 132 21 ≥+ xx ; 0, 21 ≥xx .
5) 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. Formulate this problem as LPP in order to maximize the profit? [06]
__________X__________
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 10 / 09 / 2012
Page-1
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1
(Session: 2012-13)
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) Explain slack and surplus variables with example used in LPP. (Q. No. 4-i) [02+02]
2) Solve the following LPP using simplex method
10834 321 ≤++− xxx
0,, 321 ≥xxxand (Q. No.5) [06]
Part – B
[20 Marks]
3) Solve the following linear programming problem: [08]
Min Z = x1 - 2x2 - 3x3 subject to -2x1 + x2 + 3x3 = 2; 2x1 + 3x2 + 4x3 = 1 and x1, x2, x3 ≥ 0.
4) Solve the following linear programming problem graphically: [06]
Min. 21 25 xxZ −= s. t. 132 21 ≥+ xx ; 0, 21 ≥xx .
5) 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. Formulate this problem as LPP in order to maximize the profit? [06]
__________X__________
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
42;723.23 21321321 +−≤+−+−= xxxxxtsxxxzMin
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 10 / 09 / 2012
Page-1
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-1
(Session: 2012-13)
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) Solve the linear programming problem graphically:
Maximize 21 45 xxz += s. t. 0,;705.12;805.25.1 212121 ≥≤+≤+ xxxxxx . (Q. No. 4-ii) [04]
2) Use Big-M method to maximize: 213 xxz −= s. t. 22 21 ≥+ xx ; 33 21 ≤+ xx ; 42 ≤x and 0, 21 ≥xx .
(Q. No.7) [06]
Part – B [20 Marks]
3) Use Simplex method to solve: [08]
Max. Z = 2x1 + x2 subject to x1 - x2 ≤ 10; 2x1 – x2 ≤ 40; x1, x2 ≥ 0.
4) What is operations research? Explain general method for solving operations research models. [02+04]
5) 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. Formulate this problem as LPP in order to maximize the profit? [06]
__________X__________
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-02
(Session: 2012-13)
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) Write the dual of the following primal problem [05]
Min z = 3x1 - 2x2 + x3 s.t. 2x1 - 3x2 + x3 ≤ 5; 4x1 - 2x2 ≥ 9; -8x1 + 4x2 + 3x3 = 8 and x1, x2 ≥ 0,
x3 is unrestricted in sign (Q. No. 9-ii T1)
2) A college department chairman has the problem of providing teachers for all courses offered by his
department 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. [05]
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
How should he assign his staff to the courses to maximize educational quality in his department?
` (Q. No.7 T2)
Part – B [20 Marks]
3) Use dual simplex method to solve the following LPP [7.5]
.0,,,;852;1065;124365..5376
43214321
43243214321
≥≥+++≥−+≥+−++++=
xxxxxxxxxxxxxxxtsxxxxzMin
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-2 of 2
4) A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G
and H. Monthly plant capacities are 800, 500 and 900 units respectively. Monthly warehouse
requirements are 400, 400, 500, 400 and 800 units respectively. Unit transportation costs (in Rupees) are
given below. [7.5]
To
D E F G H
A 5 8 6 6 3
B 4 7 7 6 5
C 8 4 6 6 4
Determine an optimum distribution for the company in order to minimize the total transportation
cost.
5) Formulate the following assignment problem as a linear programming model. [05]
A B C D I 5 7 11 6 II 8 5 9 6 III 4 7 10 7 IV 10 4 8 3
__________X__________
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-02
(Session: 2012-13)
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) Consider the following transportation problem: [02+02+02]
It is not possible to transport any quantity from factory B to Godown 5.
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. (Q. No. 3 T2)
2) There are 5 jobs to be assigned, one each to 5 persons and the profit for each person on each job is
given as: Person [04]
Job
Find the optimal assignment to maximize the profit. (Q. No. 5 T2)
Academic/26 Refer/WI/ACAD/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
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
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-2 of 2
Part – B [20 Marks]
3) Use dual simplex method to solve the following LPP [7.5]
.0,,,;852;1065;124365..5376
43214321
43243214321
≥≥+++≥−+≥+−++++=
xxxxxxxxxxxxxxxtsxxxxzMin
4) A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G
and H. Monthly plant capacities are 800, 500 and 900 units respectively. Monthly warehouse
requirements are 400, 400, 500, 400 and 800 units respectively. Unit transportation costs (in Rupees) are
given below. [7.5]
To
D E F G H
A 5 8 6 6 3
B 4 7 7 6 5
C 8 4 6 6 4
Determine an optimum distribution for the company in order to minimize the total transportation cost.
5) Write the dual of the following LPP [05]
.0,;10834;1242;723..23 2132121321321 ≥=++−≥−≤+−−−= xxxxxxxxxxtsxxxzMin
__________X__________
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-02
(Session: 2012-13)
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) Use dual simplex method to solve [06]
0,;3;102;7;123 21221212121 ≥≤≥+≤+≥+−−= xxxxxxxxxtosubjectxxzMax (Q. No.10 T1)
2) Write the various steps involved in MODI method. (Q. No.1 T2) [04]
Part – B
[20 Marks]
3) A company has one surplus truck in each of the cities A, B, C, D and E and one deficit truck in each of
the cities 1, 2, 3, 4, 5 and 6. The distance between the cities in kilometers is shown in the matrix below.
Find the assignment of trucks from cities in surplus to cities in deficit so that the total distance covered
by vehicles is minimum. [7.5]
1 2 3 4 5 6
A
B
C
D
E
Academic/26 Refer/WI/ACAD/18
12 10 15 22 18 8
10 18 25 15 16 12
11 10 3 8 5 9
6 14 10 13 13 12
8 12 11 7 13 10
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-2 of 2
4) A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G
and H. Monthly plant capacities are 800, 500 and 900 units respectively. Monthly warehouse
requirements are 400, 400, 500, 400 and 800 units respectively. Unit transportation costs (in Rupees) are
given below. [7.5]
To
D E F G H
A 5 8 6 6 3
B 4 7 7 6 5
C 8 4 6 6 4
Determine an optimum distribution for the company in order to minimize the total transportation cost.
5) Write the dual of the following LPP [05]
.0,;10834;1242;723..23 2132121321321 ≥=++−≥−≤+−−−= xxxxxxxxxxtsxxxzMin
__________X__________
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-02
(Session: 2012-13)
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 company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly
company capacities are 200, 160 and 90 units, respectively. Weekly warehouse requirement are 180,120
and 150 units, respectively. Units shipping costs (in Rupees) are as follows: [05]
Determine the optimal distribution for this company to minimize total shipping cost. (Q. No. 4 T2)
2) A department has five employers with five jobs to be performed. The time (in hours) each men will take
to each job is given in the effective matrix. How should the jobs be allocated, one per employer, so as to
minimize the total man hour? [05]
Jobs Employers
E1 E2 E3 E4 E5 A 10 5 13 15 16 B 3 9 18 13 6 C 10 7 2 2 2 D 7 11 9 7 12 E 7 9 10 4 12
(Q. No. 6 T2)
Academic/26 Refer/WI/ACAD/18
W W W Supply F 16 20 12 200 F 14 8 18 160 F 26 24 16 90 Demand 180 120 150 450
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-2 of 2
Part – B
[20 Marks]
3) Use dual simplex method to solve the following LPP [7.5]
.0,,,;852;1065;124365..5376
43214321
43243214321
≥≥+++≥−+≥+−++++=
xxxxxxxxxxxxxxxtsxxxxzMin
4) A company has one surplus truck in each of the cities A, B, C, D and E and one deficit truck in each of
the cities 1, 2, 3, 4, 5 and 6. The distance between the cities in kilometers is shown in the matrix below.
Find the assignment of trucks from cities in surplus to cities in deficit so that the total distance covered
by vehicles is minimum. [7.5]
1 2 3 4 5 6
A
B
C
D
E
5) Write the dual of the following LPP [05]
.0,;10834;1242;723..23 2132121321321 ≥=++−≥−≤+−−−= xxxxxxxxxxtsxxxzMin
__________X__________
12 10 15 22 18 8
10 18 25 15 16 12
11 10 3 8 5 9
6 14 10 13 13 12
8 12 11 7 13 10
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-02
(Session: 2012-13)
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) Write the dual of the following primal problem: [05]
.,0;10;82;22..24. 2121212121 signinedunrestrictxxxxxxxxtsxxzMax ≥≤−=+≥−+=
(Q. No. 9-i T1)
2) Discuss the Hungarian method of solving an assignment problem for minimization. [05]
(Q. No.2 T2)
Part – B [20 Marks]
3) A company has one surplus truck in each of the cities A, B, C, D and E and one deficit truck in each of
the cities 1, 2, 3, 4, 5 and 6. The distance between the cities in kilometers is shown in the matrix below.
Find the assignment of trucks from cities in surplus to cities in deficit so that the total distance covered
by vehicles is minimum. [7.5]
1 2 3 4 5 6
A
B
C
D
E
Academic/26 Refer/WI/ACAD/18
12 10 15 22 18 8
10 18 25 15 16 12
11 10 3 8 5 9
6 14 10 13 13 12
8 12 11 7 13 10
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 01 / 10 / 2012
Page-2 of 2
4) A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G
and H. Monthly plant capacities are 800, 500 and 900 units respectively. Monthly warehouse
requirements are 400, 400, 500, 400 and 800 units respectively. Unit transportation costs (in Rupees) are
given below. [7.5]
To
D E F G H
A 5 8 6 6 3
B 4 7 7 6 5
C 8 4 6 6 4
Determine an optimum distribution for the company in order to minimize the total transportation cost.
5) Use dual simplex method to solve the following LPP [05]
0,1;22 21212121 ≥≥−−≥++= xxandxxxxtosubjectxxzMin
__________X__________
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-03
(Session: 2012-13)
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 small project is composed of seven activities whose time estimates are listed in the table as [05]
follows: Activity
i-j Estimated Duration (in weeks)
Optimistic Most likely Pessimistic 1-2 1 1 7 1-3 1 4 7 1-4 2 2 8 2-5 1 1 1 3-5 2 5 14 4-6 2 5 8 5-6 3 6 15
i) Draw the project network.
ii) Find the expected duration and variance of each activity.
iii) What is the expected project length?
iv) Find critical path.
v) Calculate the variance and standard deviation of project length. (Q. No. 6 T3)
2) What do you understand by sequencing problem? Give three different examples of sequencing problems
of our daily life. (Q. No. 8 T2) [05]
Part – B [20 Marks]
3) The utility data for a network are given below. Determine the total, free, independent and interfering
floats. Identify the critical path and project duration. [06]
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
P. T. O.
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-2 of 2
4) A small project consisting of eight activities has the following characteristics: [08]
Activity A B C D E F G H
Preceding Activity - - A A A B, C D E, F, G
Time
Estimates
(in weeks)
Optimistic
time (to)
2 10 8 10 7 9 3 5
Most likely
time(tm)
4 12 9 15 7.5 9 3.5 5
Pessimistic
time(tp)
12 26 10 20 11 9 7 5
(a) Draw the PERT network for the project.
(b) Determine the critical path and the expected project length.
(c) Calculate the variance and standard deviation of the project length.
(d) If a 30 weeks deadline is imposed, what is the probability that the project will be finished in time?
(e) If the project manager wants to be 99%, sure that the project is completed on the schedule date, how
many weeks before that data should he start the project work?
5) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for both machine. [06]
.
__________X__________
Tasks A B C D E F G H I
Time on machine-I 2 5 4 9 6 8 7 5 4
Time on machine-II 6 8 7 4 3 9 3 8 11
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-03
(Session: 2012-13)
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) Tasks A,B,C,…..H,I constitute a project. The notation X<Y means that the task X must be finished
before Y can begin. With this notation A<D, A<E, B<F, D<F, C<G, C<H, F<I, G<I [05]
Draw a graph to represent the sequence of tasks and find minimum time of completion of the project,
when the time (in days) of completion of each task is as follows:
Task: A B C D E F G H I
Time: 8 10 8 10 16 17 18 14 9 (Q. No. 3 T3)
2) 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. [05]
(Q. No. 10 T2)
Part – B [20 Marks]
3) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for both machine. [06]
P. T. O.
Academic/26 Refer/WI/ACAD/18
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
Tasks A B C D E F G H I
Time on machine-I 2 5 4 9 6 8 7 5 4
Time on machine-II 6 8 7 4 3 9 3 8 11
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-2 of 2
4) A small project consisting of eight activities has the following characteristics: [08]
Activity A B C D E F G H
Preceding Activity - - A A A B, C D E, F, G
Time
Estimates
(in weeks)
Optimistic
time (to)
2 10 8 10 7 9 3 5
Most likely
time(tm)
4 12 9 15 7.5 9 3.5 5
Pessimistic
time(tp)
12 26 10 20 11 9 7 5
(a) Draw the PERT network for the project.
(b) Determine the critical path and the expected project length.
(c) Calculate the variance and standard deviation of the project length.
(d) If a 30 weeks deadline is imposed, what is the probability that the project will be finished in time?
(e) If the project manager wants to be 99%, sure that the project is completed on the schedule date, how
many weeks before that data should he start the project work?
5) The utility data for a network are given below. Determine the total, free, independent and interfering floats. Identify the critical path and project duration. [06]
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
__________X__________
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-03
(Session: 2012-13)
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) Explain the following terms used in PERT: (i) Pessimistic time (ii) Optimistic time (iii) Most likely
time. (Q. No. 1 T3) [05]
2) There are six jobs, first over machine I and then over II. The order of the completion of jobs has no
significance. The following table gives the machine times in hours for six jobs and the two machines.
Job No.→ 1 2 3 4 5 6 Machine I 5 9 4 7 8 6 Machine II 7 4 8 3 9 5
Find the sequence of the jobs that minimizes the total elapsed time to complete the jobs. Find the minimum time also. (Q. No. 9 T2) [05]
Part – B
[20 Marks]
3) The utility data for a network are given below. Determine the total, free, independent and interfering floats. Identify the critical path and project duration. [06]
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
P. T. O.
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-2 of 2
4) A small project consisting of eight activities has the following characteristics: [08]
Activity A B C D E F G H
Preceding Activity - - A A A B, C D E, F, G
Time
Estimates
(in weeks)
Optimistic
time (to)
2 10 8 10 7 9 3 5
Most likely
time(tm)
4 12 9 15 7.5 9 3.5 5
Pessimistic
time(tp)
12 26 10 20 11 9 7 5
(a) Draw the PERT network for the project.
(b) Determine the critical path and the expected project length.
(c) Calculate the variance and standard deviation of the project length.
(d) If a 30 weeks deadline is imposed, what is the probability that the project will be finished in time?
(e) If the project manager wants to be 99%, sure that the project is completed on the schedule date, how
many weeks before that data should he start the project work?
5) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for each machine. [06]
__________X__________
Tasks A B C D E F G
Time on machine-I 3 8 7 4 9 8 7
Time on machine-II 4 3 2 5 1 4 3
Time on machine-III 6 7 5 11 5 6 12
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-03
(Session: 2012-13)
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 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. (Q. No. 8 T3)
2) Discuss in brief PERT, CPM and dummy activities with reference to Project Management. [05]
(Q. No. 2 T3)
Part – B
[20 Marks]
3) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for both machine. [06]
P. T. O.
Academic/26 Refer/WI/ACAD/18
Tasks A B C D E F G H I
Time on machine-I 2 5 4 9 6 8 7 5 4
Time on machine-II 6 8 7 4 3 9 3 8 11
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-2 of 2
4) A small project consisting of eight activities has the following characteristics: [08]
Activity A B C D E F G H
Preceding Activity - - A A A B, C D E, F, G
Time
Estimates
(in weeks)
Optimistic
time (to)
2 10 8 10 7 9 3 5
Most likely
time(tm)
4 12 9 15 7.5 9 3.5 5
Pessimistic
time(tp)
12 26 10 20 11 9 7 5
(a) Draw the PERT network for the project.
(b) Determine the critical path and the expected project length.
(c) Calculate the variance and standard deviation of the project length.
(d) If a 30 weeks deadline is imposed, what is the probability that the project will be finished in time?
(e) If the project manager wants to be 99%, sure that the project is completed on the schedule date, how
many weeks before that data should he start the project work?
5) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for each machine. [06]
__________X__________
Tasks A B C D E F G
Time on machine-I 3 8 7 4 9 8 7
Time on machine-II 4 3 2 5 1 4 3
Time on machine-III 6 7 5 11 5 6 12
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-03
(Session: 2012-13)
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 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) Calculate total float for each activity. (Q. No. 4 T3)
2) The following are the details of estimated times of activities of a certain project. [05]
Activity A B C D E F Immediate predecessors
- A A B,C - E
Estimated time(weeks)
2 3 4 6 2 8
P. T. O.
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 22 / 10 / 2012
Page-2 of 2
(a) Find the critical path and the expected time of the project. (b) Calculate the earliest start time and earliest finish time for each activity. (c) Calculate the slack for each activity. (Q. No. 11 T3)
Part – B [20 Marks]
3) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for both machine. [06]
4) A small project consisting of eight activities has the following characteristics: [08]
Activity A B C D E F G H
Preceding Activity - - A A A B, C D E, F, G
Time
Estimates
(in weeks)
Optimistic
time (to)
2 10 8 10 7 9 3 5
Most likely
time(tm)
4 12 9 15 7.5 9 3.5 5
Pessimistic
time(tp)
12 26 10 20 11 9 7 5
(a) Draw the PERT network for the project.
(b) Determine the critical path and the expected project length.
(c) Calculate the variance and standard deviation of the project length.
(d) If a 30 weeks deadline is imposed, what is the probability that the project will be finished in time?
(e) If the project manager wants to be 99%, sure that the project is completed on the schedule date, how
many weeks before that data should he start the project work?
5) Find the sequence that minimizes the total elapsed time required to complete the following tasks, also
find elapsed time and idle time for each machine. [06]
__________X__________
Tasks A B C D E F G H I
Time on machine-I 2 5 4 9 6 8 7 5 4
Time on machine-II 6 8 7 4 3 9 3 8 11
Tasks A B C D E F G
Time on machine-I 3 8 7 4 9 8 7
Time on machine-II 4 3 2 5 1 4 3
Time on machine-III 6 7 5 11 5 6 12
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-04
(Session: 2012-13)
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) 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.
(Q. No. 3) [05]
2) A TV repairman finds that the time spent on his jobs has an exponential distribution with mean 30
minutes. If he repairs sets in the order in which they came in, and if the arrival of sets is approximately
Poisson with an average rate of 10 per 8 hour day, what is repairman’s expected idle time each day?
How many jobs are ahead of the average set just brought? (Q. No. 10) [05]
Part – B [20 Marks]
3) In a certain game player has three possible courses of action L, M and N, while B has two possible
choices P and Q. Payments to be made according to the choice made. [06]
Choices Payments L,P A pays B Rs.3 L,Q B pays A Rs. 3 M,P A pays B Rs.2 M,Q B pays A Rs.4 N,P B pays A Rs.2 N,Q B pays A Rs.3
What are the best strategies for players A and B in this game? What is the value of the game for A and
B?
4) On an average 96 patients per 24-hour day require the service of an emergency clinic. Also on an
average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one
emergency at a time. Suppose that it costs the clinic Rs. 100/- per patient treated to obtain an average
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-2 of 2
servicing time of 10 minutes, and that each minute of decrease in this average time would costs Rs. 10/-
per patient treated. How much would have to be budgeted by the clinic to decrease the average size of
the queue from 311 patients to
21 a patient. [06]
5) For the following payoff matrix, transform the zero-sum game into an equivalent linear programming
problem and solve it by using simplex method. [08]
Player B
Player A
__________X__________
B1 B2 B3 A1 1 -1 3 A2 3 5 -3 A3 6 2 -2
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-04
(Session: 2012-13)
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 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. (Q. No. 4) [05]
2) A telephone exchange has two long distance operators. The telephone company finds that, during the
peak load, long distance calls arrive in Poisson fashion at an average rate of 15 per hrs. The length of the
service on these calls is approximately exponentially distributed with mean length of 5 minutes.
(a) What is the probability that a subscriber will have to wait for his long distance call during the peak
hrs of the day? (b) If the subscribers will wait and serviced in turn, what is the expected waiting time?
(Q. No. 9) [05]
Part – B [20 Marks]
3) In a certain game player has three possible courses of action L, M and N, while B has two possible
choices P and Q. Payments to be made according to the choice made. [06]
Choices Payments L,P A pays B Rs.3 L,Q B pays A Rs. 3 M,P A pays B Rs.2 M,Q B pays A Rs.4 N,P B pays A Rs.2 N,Q B pays A Rs.3
What are the best strategies for players A and B in this game? What is the value of the game for A and B?
4) On an average 96 patients per 24-hour day require the service of an emergency clinic. Also on an
average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one
emergency at a time. Suppose that it costs the clinic Rs. 100/- per patient treated to obtain an average
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-2 of 2
servicing time of 10 minutes, and that each minute of decrease in this average time would costs Rs. 10/-
per patient treated. How much would have to be budgeted by the clinic to decrease the average size of
the queue from 311 patients to
21 a patient. [06]
5) For the following payoff matrix, transform the zero-sum game into an equivalent linear programming
problem and solve it by using simplex method. [08]
Player B
Player A
__________X__________
B1 B2 B3 A1 1 -1 3 A2 3 5 -3 A3 6 2 -2
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-04
(Session: 2012-13)
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) Solve the following games graphically.
Player B
Player A
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−−−−
1234976521
(Q. No. 5-ii) [05]
2) If for a period of two hrs. in the day (8-10 A.M.), trains arrive at the yard every 20 minutes but the
service time continuous to remain 36 minutes. Then calculate for this period (a) the probability that yard
is empty. (b) Average queue length, on the assumption that the line capacity of the yard is limited to 4
trains only. (Q. No. 8) [05]
Part – B [20 Marks]
3) In a certain game player has three possible courses of action L, M and N, while B has two possible
choices P and Q. Payments to be made according to the choice made. [06]
Choices Payments L,P A pays B Rs.3 L,Q B pays A Rs. 3 M,P A pays B Rs.2 M,Q B pays A Rs.4 N,P B pays A Rs.2 N,Q B pays A Rs.3
What are the best strategies for players A and B in this game? What is the value of the game for A and
B?
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-2 of 2
4) On an average 96 patients per 24-hour day require the service of an emergency clinic. Also on an
average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one
emergency at a time. Suppose that it costs the clinic Rs. 100/- per patient treated to obtain an average
servicing time of 10 minutes, and that each minute of decrease in this average time would costs Rs. 10/-
per patient treated. How much would have to be budgeted by the clinic to decrease the average size of
the queue from 311 patients to
21 a patient. [06]
5) For the following payoff matrix, transform the zero-sum game into an equivalent linear programming
problem and solve it by using simplex method. [08]
Player B
Player A
__________X__________
B1 B2 B3 A1 1 -1 3 A2 3 5 -3 A3 6 2 -2
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-04
(Session: 2012-13)
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) 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? (Q. No. 6) [05]
2) A self-service store employs one cashier at its counter. An average of nine customers arrives every 5
minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival
rate an exponential distribution for service rate, find (i) average number of customer in the system (ii)
average number of customer in queue or average queue length (iii) average time a customer spends in
the system (iv) average time a customer waits before being served. (Q. No. 11) [05]
Part – B
[20 Marks]
3) In a certain game player has three possible courses of action L, M and N, while B has two possible
choices P and Q. Payments to be made according to the choice made. [06]
Choices Payments L,P A pays B Rs.3 L,Q B pays A Rs. 3 M,P A pays B Rs.2 M,Q B pays A Rs.4 N,P B pays A Rs.2 N,Q B pays A Rs.3
What are the best strategies for players A and B in this game? What is the value of the game for A and B?
4) On an average 96 patients per 24-hour day require the service of an emergency clinic. Also on an
average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-2 of 2
emergency at a time. Suppose that it costs the clinic Rs. 100/- per patient treated to obtain an average
servicing time of 10 minutes, and that each minute of decrease in this average time would costs Rs. 10/-
per patient treated. How much would have to be budgeted by the clinic to decrease the average size of
the queue from 311 patients to
21 a patient. [06]
5) For the following payoff matrix, transform the zero-sum game into an equivalent linear programming
problem and solve it by using simplex method. [08]
Player B
Player A
__________X__________
B1 B2 B3 A1 1 -1 3 A2 3 5 -3 A3 6 2 -2
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-1 of 2
SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT
B. Tech. [SEM VII (CE, ME, IT, EI, EN, CS & EC – All Groups)] QUIZ TEST-04
(Session: 2012-13)
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) Solve the following games graphically.
Player B
Player A ⎥⎦
⎤⎢⎣
⎡ −23012012
(Q. No. 5-i) [05]
2) Regarding queue system, explain the following: (i) Balking, reneging & jockeying, (ii) steady state &
transient state. (Q. No. 7-iv & vi) [05]
Part – B
[20 Marks] 3) In a certain game player has three possible courses of action L, M and N, while B has two possible
choices P and Q. Payments to be made according to the choice made. [06]
Choices Payments L,P A pays B Rs.3 L,Q B pays A Rs. 3 M,P A pays B Rs.2 M,Q B pays A Rs.4 N,P B pays A Rs.2 N,Q B pays A Rs.3
What are the best strategies for players A and B in this game? What is the value of the game for A and B?
4) On an average 96 patients per 24-hour day require the service of an emergency clinic. Also on an
average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one
emergency at a time. Suppose that it costs the clinic Rs. 100/- per patient treated to obtain an average
servicing time of 10 minutes, and that each minute of decrease in this average time would costs Rs. 10/-
per patient treated. How much would have to be budgeted by the clinic to decrease the average size of
the queue from 311 patients to
21 a patient. [06]
Academic/26 Refer/WI/ACAD/18
Time: 1 Hour Max. Marks: 30
EOE-073/ Mr. S. B. Tiwari, Mr. J. P. Ojha, Mr. A. K. Mishra, Dr. Akhilesh Mishra & Mr. Rupesh Srivastav. Date: 17 / 11 / 2012
Page-2 of 2
5) For the following payoff matrix, transform the zero-sum game into an equivalent linear programming
problem and solve it by using simplex method. [08]
Player B
Player A
__________X__________
B1 B2 B3 A1 1 -1 3 A2 3 5 -3 A3 6 2 -2