problem1)
describe the scope of the Operations Research. Describe the features of Operations Research?
problem2)
Six Operators are to be assigned to five jobs with cost of assignment in Rs. given in matrix below. Determine optimal assignment. Which operator will have no assignment?
                                                       Operators
Jobs
                                          1        2           3          4          5
1                                        6        2           5          2          6
2                                        2        5           8          7          7
3                                        7        8           6          9          8
4                                        6        2           3          4          5
5                                        9        3           8          9          7
6                                        4        7           4          6          8

problem3)

a) describe Monte Carlo Simulation.
b) Company produces 150 cars. But production rate varies with distribution.

Production Rate            147          148      149       150       151       152     153
Probability                    0.05          0.10     0.15      0.20      0.30      0.15    0.05

At present the track will hold 150 cars. Using following random numbers find out the average number of cars waiting for the shipment in a company and average number of empty space in a truck. Random Numbers 82, 54, 50, 96, 85, 34, 30, 02, 64, 47.

problem4)

describe Characteristics and Constituents of the Queuing System.

problem5)

a) What do you understand by dominance? State dominance rules for the rows and columns.
b) Find saddle point of the following game and state the optimum strategies for players A and B
                                                                  A
B
                           1                    2             3             4                5
1                         9                    3             1             8                0
2                         6                    5             4             6                 7
3                         2                    4             4             3                 8
4                         5                    6             2             2                 1

problem6)

a) prepare differences between PERT and CPM?

b) A project has eleven activities whose duration is given in the following table:

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

i) Draw the network
ii) Identify the critical activities and critical path.