BA9226 APPLIED OPERATIONS RESEARCH FOR MANAGEMENT NOVEMBER/DECEMBER 2010 ANNA UNIVERSITY MBA QUESTION PAPER NOV/DEC 2010 REGULATION 2009
BA9226 APPLIED OPERATIONS RESEARCH FOR MANAGEMENT NOVEMBER/DECEMBER 2010 ANNA UNIVERSITY MBA QUESTION PAPER NOV/DEC 2010 REGULATION 2009
2. What is sensitivity analysis?
3. List the methods used to arrive at an initial basic feasible solution in a
transportation model.
4. How does a travelling salesman problem differ from a routine assignment
model?
5. Define zero sum game.
6. What is a mixed integer programming problem?
7. Define simulation.
8. What is meant by EOL?
9. What is the significance of ‘r’ in a replacement model?
10. List the applications of queuing models.
PART B — (5 × 16 = 80 Marks)
11. (a) A person requires 10, 12, and 12 units of a dry and liquid combination of
chemicals A, B and C respectively for his garden. A liquid product
contains 5, 2 and 1 units of A, B and C respectively per jar. A dry product
contains 1, 2 and 4 units of A, B and C per carton. If the liquid product
sells for Rs. 3 per jar and the dry product sells for Rs. 2 per carton, how
many of each should he purchase in order to minimize the cost and meet
the requirement? (16)
Or
(b) Maximise z = z y x 3 2 5 + −
Subject to:
0 , ,
5 3
3 4 3
2 2 2
>=
<= +
<= −
>= − +
z y x
z y
y x
z y x
(16)
12. (a) Find the minimum cost distribution plan to satisfy demand for cement at
three construction sites from available capacities at the three cement
plants given the following transportation costs (in Rs) per ton of cement
moved from plants to sites.
From To construction sites Capacity (tons / month)
1 2 3
P1 300 360 425 600
P2 390 340 310 300
P3 255 295 275 1000
Demand (tons/month) 400 500 800
Or
(b) A company is faced with the problem of assigning 4 machines to
6 different jobs (one machine to one job only). The profits are estimated
as follows. Solve the problem to maximize the total profits.
Job Machine
A B C D
1 3 6 2 6
2 7 1 4 4
3 3 8 5 8
4 6 4 3 7
5 5 2 4 3
6 5 7 6 4
13. (a) Solve Max z = y x 4 +
subject to : 2x + 4y < = 7, 5x + 3y < = 15, where x and y are positive
integers.
Or
132 132 132
96515 3
(b) Solve the following game whose payoff matrix is given below.
Player B
Player
A
B1 B2 B3 B4
A1 5 –10 9 0
A2 6 7 8 1
A3 8 7 15 2
A4 3 4 -1 4
14. (a) The annual demand for a product is 100000 units. The rate of production
is 200000 units per year. The set-up cost per production run is Rs. 5000
and the variable production cost of each item is Rs 10. The annual
holding cost per unit is 20% of its value. Find the optimum production lot
size and the length of the production run.
Or
(b) A manager has a choice between
(i) A risky contract promising Rs 7 lakhs with probability 0.6 and
Rs. 4 lakhs with probability 0.4 and
(ii) A diversified portfolio consisting of two contracts with independent
outcomes each promising Rs 3.5 lakhs with probability 0.6 and
Rs. 2 lakhs with probability 0.4. Using the EMV criteria suggest a
contract.
15. (a) There are two clerks in a university to receive fees from the students. If
the service time for each student is exponential with mean 4 minutes and
if the boys arrive in a Poisson fashion at the counter at the rate of 10 per
hour, determine
(i) The probability of having to wait for service (8)
(ii) The expected percentage idle time for each clerk. (8)
Or
(b) The probability Pn of failure just before age ‘n’ is shown below for
1000 bulbs. If the individual replacement costs Rs. 1 and the group
replacement costs Rs. 0.3 per item, find the optimal replacement policy.
n : 1 2 3 4 5
Pn : 0.3 0.1 0.1 0.2 0.3
BA9226 APPLIED OPERATIONS RESEARCH FOR MANAGEMENT NOVEMBER/DECEMBER 2010 ANNA UNIVERSITY MBA QUESTION PAPER NOV/DEC 2010 REGULATION 2009
M.B.A. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010
Second Semester
BA 9226 — APPLIED OPERATIONS RESEARCH FOR MANAGEMENT
(Regulation 2009)
Time : Three hours Maximum : 100 Marks
Answer ALL questions
PART A — (10 × 2 = 20 Marks)
1. List the scope of applications of OR techniques.2. What is sensitivity analysis?
3. List the methods used to arrive at an initial basic feasible solution in a
transportation model.
4. How does a travelling salesman problem differ from a routine assignment
model?
5. Define zero sum game.
6. What is a mixed integer programming problem?
7. Define simulation.
8. What is meant by EOL?
9. What is the significance of ‘r’ in a replacement model?
10. List the applications of queuing models.
PART B — (5 × 16 = 80 Marks)
11. (a) A person requires 10, 12, and 12 units of a dry and liquid combination of
chemicals A, B and C respectively for his garden. A liquid product
contains 5, 2 and 1 units of A, B and C respectively per jar. A dry product
contains 1, 2 and 4 units of A, B and C per carton. If the liquid product
sells for Rs. 3 per jar and the dry product sells for Rs. 2 per carton, how
many of each should he purchase in order to minimize the cost and meet
the requirement? (16)
Or
(b) Maximise z = z y x 3 2 5 + −
Subject to:
0 , ,
5 3
3 4 3
2 2 2
>=
<= +
<= −
>= − +
z y x
z y
y x
z y x
(16)
12. (a) Find the minimum cost distribution plan to satisfy demand for cement at
three construction sites from available capacities at the three cement
plants given the following transportation costs (in Rs) per ton of cement
moved from plants to sites.
From To construction sites Capacity (tons / month)
1 2 3
P1 300 360 425 600
P2 390 340 310 300
P3 255 295 275 1000
Demand (tons/month) 400 500 800
Or
(b) A company is faced with the problem of assigning 4 machines to
6 different jobs (one machine to one job only). The profits are estimated
as follows. Solve the problem to maximize the total profits.
Job Machine
A B C D
1 3 6 2 6
2 7 1 4 4
3 3 8 5 8
4 6 4 3 7
5 5 2 4 3
6 5 7 6 4
13. (a) Solve Max z = y x 4 +
subject to : 2x + 4y < = 7, 5x + 3y < = 15, where x and y are positive
integers.
Or
132 132 132
96515 3
(b) Solve the following game whose payoff matrix is given below.
Player B
Player
A
B1 B2 B3 B4
A1 5 –10 9 0
A2 6 7 8 1
A3 8 7 15 2
A4 3 4 -1 4
14. (a) The annual demand for a product is 100000 units. The rate of production
is 200000 units per year. The set-up cost per production run is Rs. 5000
and the variable production cost of each item is Rs 10. The annual
holding cost per unit is 20% of its value. Find the optimum production lot
size and the length of the production run.
Or
(b) A manager has a choice between
(i) A risky contract promising Rs 7 lakhs with probability 0.6 and
Rs. 4 lakhs with probability 0.4 and
(ii) A diversified portfolio consisting of two contracts with independent
outcomes each promising Rs 3.5 lakhs with probability 0.6 and
Rs. 2 lakhs with probability 0.4. Using the EMV criteria suggest a
contract.
15. (a) There are two clerks in a university to receive fees from the students. If
the service time for each student is exponential with mean 4 minutes and
if the boys arrive in a Poisson fashion at the counter at the rate of 10 per
hour, determine
(i) The probability of having to wait for service (8)
(ii) The expected percentage idle time for each clerk. (8)
Or
(b) The probability Pn of failure just before age ‘n’ is shown below for
1000 bulbs. If the individual replacement costs Rs. 1 and the group
replacement costs Rs. 0.3 per item, find the optimal replacement policy.
n : 1 2 3 4 5
Pn : 0.3 0.1 0.1 0.2 0.3
