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1. Paper: QUANTITATIVE TECHNIQUE (1B)
Specific Instructions:
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Answer all the four questions.
Marks allotted 100.
General Instructions:
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The Student should submit this assignment in the handwritten form (not in the typed format)
The Student should submit this assignment within the time specified by the exam dept
Each Question mentioned in this assignment should be answered within the word limit specified
The student should only use the Rule sheet papers for answering the questions.
The student should attach this assignment paper with the answered papers.
 Failure to comply with the above Five instructions would lead to rejection of assignment.
Question No 1
A. What is critical path? State the necessary sufficient conditions of critical path. Can a project
have multiple critical paths?
B. The time durations and labor requirements of different activities of a project are:
Activity Duration No of Workers
1-2
5
4
1-3
4
3

2. 1-4
2-4
2-6
3-4
3-5
4-6
5-6
3
2
8
4
4
5
10
2
6
3
5
5
3
5
Additional Information:
1. Labor rate is Rs 8 per day
2. Overhead charge for the project is Rs 50 per day
3. No activity can be started unless the needed labor force is available.
4. The firm has the option of employing 8, 9 or 10 workers.
5. Workers employed for the project would be paid for complete duration of the project.
Determine,
a. The optimal number of workers to be employed, and
b. The duration of the project, corresponding thereto.
Question No 2
A company has three plants in which it produces a standard product. It has four agencies in
different parts of the company where this product is sold. The production cost varies from
factory to factory and the selling price from market to market. The shipping cost varies from
each market to each of the agencies is known and stable. The relevant data are given in the
following table:

3. (a) Plant
Weekly Production capacity
(Units)
400
300
800
1
2
3
Unit production cost
(Rs)
18
24
20
(b) Shipping cost (in Rs) per unit:
1
2
3
From plant
To agency
2
5
4
4
1
2
8
3
3
7
6
4
4
3
2
5
(c) Agency Demand (Units) Selling Price (Rs)
1
300
32
2
400
35
3
300
31
4
500
36
Determine the optimal plan so as to maximize the profits.
Question No 3
A. A salesman makes all sales in three cities X, Y and Z only. It is known that he visits each city
on a weekly basis and never visits the same city in successive weeks. If he visits city X in a
given week, then he visits city Z in the next week. However, if he visits city Y or Z, he is twice
more likely to visit city X than the other city. Obtain the transition probability matrix. Also
determine the proportionate visits by him to each of the cities in the long run.
B. A company is using Markov theory to analyze brand switching between three different
brands of DVDs. Data has been obtained and used to estimate the following transition
matrix for the probability of moving between brands each month:
From
Brand
X
Y
Z
X
0.80
0.03
0.20
To Brand
Y
0.10
0.95
0.05
Z
0.10
0.02
0.75

4. The current (i.e. month 1) market shares are 45%, 25% and 30% for brands X, Y and Z
respectively.
a) Obtain the expected market shares after two months have elapsed.
b) What market shares can the three brands expect in the long run?
c) Would you expect the actual market shares to approach the expected long-run
prediction for the market or not? Why?
Question No 4
A. A company has just developed a new item for which it proposes to undertake a national
television promotional campaign. It has decided to schedule a series of one-minute
commercials during peak audience viewing hours of 1 to 5 P.M. To reach the widest possible
audience, the company wants to schedule one commercial on each of the networks and to
have only one commercial appear during each of the four one-hour time blocks. The
exposure ratings for each hour, which represent the number of viewers per Rs 10,000 spent,
are given below.
Viewing Hours
1-2 P.M.
2-3 P.M.
3-4 P.M.
4-5 P.M.
A
27.1
18.9
19.2
11.5
Network
B
C
D
18.1 11.3 9.5
15.5 17.1 10.6
18.5 9.9 7.7
21.4 16.8 12.8
(a) Which network should be scheduled each hour to provide the maximum audience
exposure?
(b) How would the schedule change if it is decided not to use network A between 3 P.M.