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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.C.A. DEGREE EXAMINATION - COMPUTER APPLICATIONS
FIFTH SEMESTER – APRIL 2013
CA 5953 - RESOURCE MANAGEMENT TECHNIQUES
Date : 11/05/2013
Time : 1:00 - 4:00
Dept. No.
Max. : 100 Marks
PART A
Answer ALL Questions
1.
(10 X 2 = 20 Marks)
What are slack and surplus variables?
2. When a linear programming problem is said to have unbounded solution?
3. Give the algorithm North-West
West Corner Rule for Transportation Problem.
4. Give mathematical formulation of Assignment Problem.
5. What is integer programming problem? Mention the types.
6. What is Gomory’s constraint in integer programming problem?
7. Define the following terms: i. Critical Path
II. Dummy Activity.
8. What are three time estimates of an activity? How mean and standard deviation of each activity
and the whole project is computed?
9. When a queue
ue is said to be exploded?
10. What is queue behavior?
PART B
Answer ALL Questions
(5 X 8 = 40 Marks)
Marks
11a. Solve graphically the following linear programming problem.
Maximize Z = 5x1 + 6x2
Subject to 3x1 + 4x2 ≤ 18
10x1 + 5x2 ≤ 35
x2 ≤ 4
x1 , x2 ≥ 0
(or)
11b. Solve the following linear programming problem
Minimize Z = 4x1 - 3x2
Subject to 5x1 + 3x2 ≤ 15
x1 + 3x2 ≤ 6
x1 , x2 ≥ 0
12a. A company has 3 factories and 4 warehouses. Production at each factory, capacity of each
warehouse and the unit cost of transportation from factory to warehouse are given in the following
table. Find the initial allocation by VAM.
Warehouse→
W1
W2
W3
W4
Availability
Factory↓
F1
6
3
5
4
22
F2
5
9
2
7
15
F3
5
7
8
6
8
Requirement
7
12
17
9
(or)
12b. An automobile dealer wishes to put four repairmen to four different jobs. The dealer estimated
the number of man-hours that would be required for each job. This information is given in the
following matrix. How should the jobs be allocated to the repairman so as to minimize the total time.
Job→
A
B
C
D
Men↓
1
5
3
2
8
2
7
9
2
6
3
6
4
5
7
4
5
7
7
8
13a. Describe Gomory’s cutting plane algorithm to solve pure integer programming problem.
(or)
13b. Explain branch and bound method for integer programming problem.
14a. A small project consists of 8 activities, the details of which are given below:
Activity
A
Predecessor -
B
C
D
E
F
G
H
-
A
A
C
D
B
E,F
Activity
T0
4
3
6
2
5
3
3
1
Tm
7
5
12
5
11
6
3
4
Tp
10
13
30
8
17
15
3
7
i.
Draw network diagram and find critical path.
ii.
Find mean and standard deviation of each activity.
iii.
Find mean and standard deviation of the whole project.
(or)
14b. Given the following information:
Activity
A
B
C
D
E
F
G
H
I
Predecessor
-
A
B
A
C
D
C
E,F
G,H
Duration(Days) 5
9
3
4
6
3
2
12
10
i.
Draw network diagram and determine the critical path.
ii.
For each activity, find earliest start and finish, latest start and finish, total float, free float and
independent float.
15a. In a departmental store, there is only one counter to give service. Customers arrive, on an average,
every 10 minutes. The counter clerk takes 5 minutes to attend one customer. Assuming customer arrival
follows Poisson distribution and service of clerk follows exponential distribution, find the following:
i.
Average queue length in the system waiting to get service.
ii.
Average time spent in the system.
iii.
Probability that there would be two customers in the queue.
(or)
15b. In a petrol bunk, customers arrive on an average of 5 minutes between arrival. The time interval
between the services follows a exponential distribution with mean time of 2 minutes. By how much
should the flow of customers be increased to justify the opening of second service point. The
management is willing to open the same provided the customer has to wait for 5 minutes for the service.
PART C
Answer any TWO Questions
(2 x 20 = 40 Marks)
(Question 16 is compulsory)
16a. A company manufactures two types of products A, B. Each product of type A requires 4 hours of
cutting and two 2 hours of fitting. Whereas each product of type B requires 2 hours of cutting and 5
hours of fitting. The company has 2 cutting machines and 3 fitting machines. Each machine can be put
to 40 hours per week and each fitting machine can be put to 60 hours per week. Profit on type A is Rs.3
each and on type B is Rs.4 each. The company wants to maximize its profit. Formulate this as linear
programming problem.
16b. Solve the following linear programming problem
Minimize Z = 3x1 -2x2 - x3
Subject to -x1 + 2x2 + 3x3 ≤ 7
4x1 - 2x3 ≤ 12
3x1 + 8x2 + 4x3 ≤ 10
x1 , x2 , x3 ≥ 0
17a. Write the Hungarian method for solving an assignment problem.
17b. Solve the following Travelling Salesman Problem.
To City→
A
B
C
D
A
-
7
9
5
B
7
-
4
6
C
9
4
-
8
D
5
6
8
-
From City↓
18a. List out the rules to be followed while drawing network diagram.
18b. A bank has two tellers working on savings account. The first teller handles withdrawals only. The
second teller handles deposits only. It has been found that the service time distribution for both deposits
and withdrawals is exponential distribution with mean service time 3 minutes per customer. Depositors
are found to arrive in a Poisson fashion with mean arrival rate16 per hour. Withdrawers also arrive with
mean arrival rate of 14 per hour. What would be the effect on the average waiting time for depositors and
withdrawers if each teller could handle both the services.
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