# LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
```LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.C.A. DEGREE EXAMINATION - COMPUTER APP.
FOURTH SEMESTER – NOVEMBER 2013
CA 5953 - RESOURCE MANAGEMENT TECHNIQUES
Date : 16/11/2013
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
PART A
(10 X 2 = 20 )
1. What are slack and surplus variables?
2. In simplex method, what is the condition that a solution for a L.P.P. is obtained.
3. State True or False the following:
i.
In Transportation Problem, initial allocation is unique.
ii.
North-West Corner rule is not an efficient method.
4. State Traveling Salesman Problem.
5. What are the methods of solving Integer Programming Problem.
6. In a simplex table, key row is x2 – (1/9)s1 + (2/9)s2 = 12/9. Obtain Gomary’s constraint from the
equation
7. Define the following:
i.
Critical path
ii. Dummy activity.
8. Distinguish between PERT and CPM
9. What is queue behavior?
10. In a bank, customers arrive at 10 per hour and get service 8 per hour. Is it possible to handle the
queue by single clerk? Give reason.
PART B
11a. Solve graphically the following linear programming problem.
Minimize Z = 4x1 - 3x2
Subject to 2x1 + 4x2 ≤ 16
3x1 + x2 ≥ 3
7x1 + 5x2 ≤ 35
x1 , x2 ≥ 0
(or)
(5 X 8 = 40 )
11b. Solve the following linear programming problem
Maximize Z = 2x1 - x2
Subject to 2x1 + 4x2 ≤ 16
3x1 + 2x2 ≤ 12
x1 , x2 ≥ 0
12a. Find the initial allocation to the following Transportation Problem by VAM
Destination →
Origin ↓
D1
D2
O1
O2
Requirement
7
4
11
9
4
9
D3
3
3
7
(or)
D4
Availability
2
5
3
16
14
12b. A department has 4 employees with 4 jobs to be performed. The time, in hour, each
employee will take to perform each job is given in the following matrix. How should the
jobs be allocated to the employees so as to minimize the total time.
Employee→
A
B
C
D
Job ↓
1
2
3
4
30
45
50
90
50
50
60
75
60
70
50
75
70
60
60
80
13a. Describe Gomory’s cutting plane algorithm to solve mixed I.P.P.
(or)
13b. Explain branch and bound method for I.P.P.
14a. Given the following information
Activity 1-2
1-3
2-4
3-4
3-5
3-6
4-6
5-6
Duration 6
8
8
6
10
12
8
6
(weeks)
i.
Draw network diagram and determine critical path.
ii.
For each activity, find earliest start, earliest finish, latest start, latest finish, total float, free
float and independent float.
(or)
14b. A project consists of 8 activities. The time estimate are in months.
Activity
A
B
C
D
E
F
G
H
Predecessor ------A
D
C, E
A
F
tO
6
3
6
6
2
4
2
1
tM
15
12
21
12
5
10
5
4
tP
24
21
30
12
14
22
20
7
i.
Draw the PERT network diagram and find the critical path.
ii.
Find the expected length of the critical path and its variance.
15a. T.V. repair man finds that the time spent on his jobs are exponential distribution with mean of 30
minutes. If the arrival of T.V. sets for repair follows Poisson distribution with the average rate of 10 per
8-hour day, how many jobs are waiting for service. What is the repairman’s idle time each day?
(or)
15b. in a petrol bunk, customers arrive in a Poisson fashion with an average time of 5 minutes between
arrival. The time interval between the service follows 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 service.
PART C
(Question no.16 is compulsory)
16a. Solve the L.P.P. by simplex method
Minimize Z = 2x1 + 3x2
Subject to x1 + x2 ≥ 5
x1 + 2x2 ≥ 6
x1 , x2 ≥ 0
16b. Describe MODI method to solve Transportation Problem
17a. Solve the following Transportation Problem
Warehouse→ W1
W2
W3
Factory↓
F1
11
20
7
F2
21
16
20
F3
8
12
18
Requirement 30
25
35
(2 x 20 = 40 )
W4
Availability
8
12
9
40
50
40
70
17b. A company has a team of 3 salesmen. There are 3 districts where the company wants to start its
business. After looking into the capabilities of salesman and the nature of districts, the company
estimated the profit per day (in hundreds of rupees) for each salesman and each district which is given
below. Find the allocation which maximizes the profit.
District→
A
B
C
Salesman↓
X
18
15
12
Y
11
27
20
Z
29
26
31
18a. Describe the rules of drawing network diagram
18b. What is Fulkerson’s rule of numbering the node?
18c. A supermarket has two sales girls serving at the customers. The customers arrive in a Poisson
fashion at the rate of 12 per hour. The service time for each customer is exponential distribution with
mean 6 minutes. Find
i.
The probability that an arriving customer has to wait for service.
ii.
The average number of customer in the system
iii.
The average time spent by a customer in the supermarket.
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