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Posted By: Saranya Member Level: Diamond Posted Date: 02 Jun 2008
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2007 Alagappa University M.B.A Investment Management QUANTITATIVE METHODS Question paper
DISTANCE EDUCATION
M.B.A. (IM) DEGREE EXAMINATION, DECEMBER 2007.
First Semester
QUANTITATIVE METHODS
(2005 onwards)
Time : Three hours Maximum : 100 marks
SECTION A — (5 ? 8 = 40 marks)
Answer any FIVE questions.
1. Describe the steps for solving a LP problem by using two-phase simplex method.
2. Differentiate between dynamic programming with linear programming.
3. Explain the concept of trade off.
4. A small manufacturer employs 5 skilled men and 10 semi-skilled men and makes a product is two quantities, a deluxe model and an ordinary model. The production of deluxe model requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. The ordinary model requires
1 hour work by a skilled man and 3 hours work by semi-skilled man. By union rules, no man can work more than 8 hours per day. The profit of the deluxe model is Rs. 1000 per unit and that of an ordinary model is Rs. 800 per unit. Formulate the linear programming model and solve it by graphical method.
5. Solve graphically the following LPP.
Maximize
Subject to constraints
6. Determine the break - even sales in the following case :
Product
A B C
Sales (units) 5000 6000 4000
Unit selling price (Rs.) 10 15 18
Unit variable cost (Rs) 6 4 13
Fixed cost (Rs.) 4000
7. Three players A, B and C play a sequence of games. It is so decided that winner of each game scores one point and he who first scores three points is the final winner. A wins the first and third games while B wins the second. What is the probability that C is the final winner?
8. Determine an initial basic feasible solution to the following transportation problem by least cost method.
To
1 2 3
A 10 13 6 10
From B 16 7 13 12
C 8 22 2 8
6 11 13
SECTION B — (4 ? 15 = 60 marks)
Answer any FOUR questions.
9. (a) Explain slack, surplus and artificial variables.
(b) Discuss the branch and bound method of solving Integer programming problem.
10. Use two - phase simplex method to solve
Min
Subject to constraints
and
.
11. Find the initial basic feasible solution to the following transportation problem by :
(a) Minimum cost method
(b) North - West corner rule.
State which of the methods is better
To Supply
2 7 4 5
From 3 3 1 8
5 4 7 7
1 6 2 14
Demand 7 9 18
12. Write the dual of the LPP
Maximize
Subject to
unrestricted in sign.
13. A maintenance project consists of the following jobs :
Job : 1–2 2–3 2–4 3–5 3–6 4–6 4–7 5–8 6–8 7–8
Duration (days) 2 3 5 4 1 6 2 8 7 4
(a) Draw the network
(b) Calculate the early start, early finish schedule, late start, late finish schedule.
(c) Calculate the total float and free float for each activity.
14. Two persons X and Y work on a two - station assembly line. The distributions of activity times at their stations are
Time in seconds Time frequency
for X Time frequency
for Y
10 3 2
20 7 3
30 10 6
40 15 8
50 35 12
60 18 9
70 8 7
80 4 3
(a) Simulate operation of the line for eight items
(b) Assuming Y must wait until X completes the first item before starting work, will he have to wait to process any of the other eight items?
15. The probabilities of 3 students A, B, C solving a problem in statistics are and . A problem is given to all the 3 students, what is the probability that,
(a) No one will solve the problem
(b) Only one will solve the problem
(c) At least one will solve the problem.
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