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Total No. of Questions: 11
[Total No. of Printed Pages: 13]
[Total No. of Printed Pages: 13]
OP-507
M.Sc. (REG./PVT./ATKT) Examination, 2024
(Fourth Semester)
MATHEMATICS
Paper-VIII
Operations Research-II
Time: 3 Hours
[Maximum Marks : {
Reg.: 85
Pvt.: 100
}]
Reg.: 85
Pvt.: 100
}]
Note: Attempt all questions.
Section A
(Objective Type Questions)
1.
Choose the correct answer: 10×1½=15
(i)
The transportation problem is balanced if :
- Total availability = Total requirement
- Total availability > Total requirement
- Total availability < Total requirement
- None of the above
(iv)
In an an assignment problem involving four workers and three jobs, total number of assignments possible is :
- 4
- 3
- 7
- 12
(v)
The word PERT means :
- Project Evaluation and Research Technique
- Project Evaluation and Review Technique
- Programme Evaluation and Review Techniques
- None of the above
(vi)
Which of the following is correct ?
- CPM is event oriented
- CPM is deterministic in nature
- Events marking the start of activities are called head events
- It is not possible for a network to have more than one critical path
(ix)
We get saddle point in payoff matrix (two persons zero sum game) :
- Minimum of row maxima = Maximum of column minima
- Minimum of row minima = Maximum of column minima
- Maximum of row minima = Minimum of column minima
- None of the above
(x)
Which one is not correct ?
- The value of game can be determined only if the game has a saddle point.
- The value of game can be positive, negative or zero.
- Pure strategy games are those in which both players stay with one strategy throught.
- None of the above
4.
Write rules of network construction.
Or
Write five differences between PERT and CPM.
5.
What is Simulation ? Explain, why is simulation used ?
Or
Write a short note on simulation models.
6.
Define player, strategy, optimum strategy, value of the game, payoff matrix.
Or
For the following two person zero sum game, find the value of the game.
8.
A car hire company has one car at each of five depots a, b, c, d and e. A customer requires a car in each town, namely A, B, C, D and E. Distance (in kms) between depots (origins) and towns (destinations) are given in the following distance matrix :
How should cars be assigned to customers so as to minimize the distance travelled ?
Or
Solve the non-linear programming problem :
Optimize Z = 4x12 + 2x22 + x32 - 4x1x2
Subject to the constraints :
x1 + x2 + x3 = 15
2x1 - x2 + 2x3 = 20
and
x1, x2, x3 ≥ 0
Optimize Z = 4x12 + 2x22 + x32 - 4x1x2
Subject to the constraints :
x1 + x2 + x3 = 15
2x1 - x2 + 2x3 = 20
and
x1, x2, x3 ≥ 0
9.
(i)
Draw the PERT network and find out the expected project completion time.
(ii)
What duraton will have 95% confidence for project completion ?
(For standard normal Z = 1.645 area under the standard normal curve from 0 to Z is 0.45.)
(For standard normal Z = 1.645 area under the standard normal curve from 0 to Z is 0.45.)
10.
Customer arrive at a milk booth for the required service. Assume that inter-arrival and service times are constant and given by 1.8 and 4 time units, respectively. Simulate the system by hand computations for 14 time units. What is the average waiting time per customer ? What is the percentage idle time of the facilitiy ? (Assume that the system starts at t = 0].
Or
Write various steps of Monte-Carlo Simulation procedure.
Or
Describe dominance property in the solution of games.
Two firms are competing for business under the condition so that one firms's gain is another firm's loss. Firm A's payoff matrix is given below :
Suggest optimum strategies for the two firms and the net outcome thereof.
Two firms are competing for business under the condition so that one firms's gain is another firm's loss. Firm A's payoff matrix is given below :