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**M.B.A. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010**

**Second Semester**

**BA9226 - APPLIED OPERATIONS RESEARCH FOR MANAGEMENT**

**(Regulation 2009)**

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**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 + - (16)

Subject to:

0 , ,

5 3

3 4 3

2 2 2

>=

<= +

<= -

>= - +

z y x

z y

y x

z y x

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) (16)

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 (16)

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. (16)

132 132 132

96515 3

Or

(b) Solve the following game whose pay-off matrix is given below. (16)

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. (16)

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. (8+8)

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 (ii) The expected percentage idle time for each clerk. (8+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 (16)

Pn : 0.3 0.1 0.1 0.2 0.3

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