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 2 1 3 2 15 x x Z − = s. t. 3 3 3 2 1 ≥ − − x x x ; 2 3 2 1 ≥ + − x x x and 0 , , 3 2 1 ≥ x x x . (Q. No. 8) [06] Part – B [20 Marks] 3) Use Simplex method to solve: [08] Max. Z = 2x 1 + x 2 subject to x 1 - x 2 ≤ 10; 2x 1 – x 2 ≤ 40; x 1 , x 2 ≥ 0. 4) Solve the following linear programming problem graphically: [06] Min. 2 1 2 5 x x Z − = s. t. 1 3 2 2 1 ≥ + x x ; 0 , 2 1 ≥ x x . 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
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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]
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]
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]
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
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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-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
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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]