MBAG-206
Sri Sathya Sai Institute of Higher Learning
(Deemed to be University)
Vidyagiri, Prasanthi Nilayam
Master of Business Administration
Second Semester Examinations, July 2015
Management Science
23/07/2015
Time : 3 Hours
Note:
Max. Marks : 100
1. Answer Sections A, B & C in the answer book provided.
2. Comply with the instructions given in the Main Answer Book carefully.
SECTION – A
(4x5=20 Marks)
I. Answer the following questions. Each question carries FIVE Marks.
1. Discuss the significance and scope of Management Science in Modern Management.
2. Differentiate between Multiple Optimal Solution and Unbounded Solution while solving LP problems by
Graphical Method and Simplex Method.
3. What is sensitivity analysis? How does it help you in overcoming some of the assumptions of LP?
4. Explain the basic differences between CPM and PERT applied to a network analysis. What do you
understand by “Probability of completing the project in a given time”?
SECTION – B
(4x10=40 Marks)
II. Answer ANY FOUR of the following questions. Each question carries TEN Marks.
5. a) What are the limitations of Graphical Solution to LP problems ? In what suitable circumstances can
graphical solution be useful?
b) Graph the following LP problem and indicate the optimal solution point:
Maximize z = 3x1 + 5x2
Subject to the constraints: x1 + 2x2  2000
x1 + x2  1500
x1, x2 ≥ 0
(4+6=10 Marks)
6. The following table provides all the necessary information on the availability of supply to each
warehouse, the requirement of each market, and the unit transportation cost in rupees from each
warehouse to each market.
Warehouse
A
B
C
Demand
Market
P
6
5
5
7
Q
3
9
7
12
R
5
2
8
17
S
4
7
6
9
Supply
22
15
8
45
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MBAG-206
The shipping clerk of the shipping agency has worked out the following schedule based on his own
experience: 12 units from A to Q, 1 unit from A to R, 8 units from A to S, 15 units from B to R,
a) Check if this allocation is cost optimum.
b) If not find an Optimal Schedule and minimum total transport cost?
(5 +5=10 Marks)
7. a) “An Assignment Model is a special case of Transportation Model” –Explain
b) A computer centre has three expert programmers. The centre wants three application programmes to
be developed. The head of the computer centre, after carefully studying the programmes to be
developed, estimates the computer time in minutes required by the experts for the application
programmes as follows:
Programmes
Programmers
2
100
90
140
1
120
80
110
A
B
C
3
80
110
120
[ Hint : Use Assignment model for maximization]
(4+6=10 Marks)
8. a) What is a Dual of a Primal in L.P. Problems ? Explain its utility.
b) Consider the following optimal table where S1 and S2 are slack variables added to the original
problem:
Basic
Variables
X3
x1
Z
Cj–Z
Cj=10
x1
0
1
10
0
15
x2
-1
5
30
-15
20
x3
1
0
20
0
0
S1
1/2
-1
0
0
0
S2
-1/3
1
10/3
-10/3
Solution
2
6
100
Required:
i)
Find the ranges of the objective function coefficients 𝐶1 and 𝐶2 of the variables x1 and x2
respectively, such that the optimality is unaffected.
ii) Check whether the optimality is unaffected if the profit coefficients are changed from (10,15,20)
to (7,14,15). If so, find the revised optimal solution.
(5+5=10 Marks)
9. a) Draw the Network Diagram for the data of a project given below:
b) Indicate the Critical path and the expected project completion time with probability of completing the
project within that period.
c) What would be the probability that the project can be completed in 23 weeks?
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MBAG-206
Project Activity Data
Preceded
Activity
by
A
B
C
D
E
F
G
H
A
A
B
C
D
D
F,E
Activity Durations
(Weeks)
tp
tm
to
3
3
3
9
6
3
6
4
2
8
6
4
8
6
4
0
0
0
5
4
3
8
5
2
(4+3+3=10 Marks)
SECTION –C
(2x20=40 Marks)
III. Answer ANY TWO of the following questions. Each question carries TWENTY Marks.
10. a) Discuss the role of sensitivity analysis in linear programming. As a future manager, under what
circumstances will you make use of it?
b) What are slack, surplus and artificial variables? How are they useful in interpretation of an Optimal
Simplex Table?
c)
A retired person wants to invest upto an amount of `30,000 in fixed income securities. His broker
recommends investing in two bonds. Bond A yielding 7% and Bond B yielding 10 %. After some
consideration he decides to invest at most `12,000 in Bond B and at least `6,000 in Bond A. He also
wants the amount invested in Bond A to be at least equal to the amount invested in Bond B. What
should the broker recommend if the investor wants to maximise his return on investment?
(6+4+10=20 Marks)
11. a) Write a short notes on degeneracy and unbounded solution.
b) A company produces three products, P1, P2 and P3 from two raw materials A and B, and Labour L.
One unit of product P1 requires one unit of A, 3 units of B and 2 units of L. One unit of Product P2
requires 2 units of A and B each, and 3 units of L, while one unit of P3 needs 2 units of A, 6 units of
B and 4 units of L. The company has a daily availability of 8 units of A, 12 units of B and 12 units of
L. It is further known that the unit contribution margin for the products is ` 3,2, and 5 respectively for
P1, P2, and P3.
Determine the optimum product mix. Is the solution obtained by you unique?
(5+15= 20 Marks)
12. a) “PERT takes care of uncertain durations”. How far is this statement correct? Explain with reasons.
b) The following network diagram represents activities associated with a project:
Activities
Optimistic
time
Pessimistic
time
Most
likely time
A
B
C
D
E
F
G
H
I
5
18
26
16
15
6
7
7
3
10
22
40
20
25
12
12
9
5
8
20
33
18
20
9
10
8
4
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MBAG-206
Determine the following:
i)
Expected time and variance
ii) The earliest and latest expected completion time of each event.
iii) The critical path
iv) The probability of expected completion time of the project if the original scheduled time of
completing the project is 41.5 weeks
v) The duration of the project that will have 95 percent chance of being completed.
(5+15=20 Marks)
*****
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