Nr410301 Operations Research

RR

Code No: RR410301

IV B.Tech I Semester(RR) Supplementary Examinations, December 2009 OPERATIONS RESEARCH (Mechanical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Discuss the scope and significance of OR in business (b) Explain the duality theory of linear programming

[8+8]

2. Solve the following transportation problem X Y Z Availability A 8 7 3 60 B 3 8 9 70 C 11 3 5 80 Demand 50 80 80

[16]

3. (a) “Operations Research replaces management by personality” discuss. (b) State the general rules for converting a primal problem into its dual. 4. There are 1000 bulbs in the system. Survival rate is given below Week 0 1 2 3

[3+13]

4

Bulbs in operation at the end of the week 1000 850 500 200 00 The group replacement of 100 bulbs costs Rs.1000 and individual replacement is Rs.20 per bulb. Suggest suitable replacement policy. [16] 5. (a) Briefly explain “dominance property” (b) A and B play game in which each has three coins 5p,10p and a 20p. Each selects a coin without the knowledge of the others choice. If the sum of the coins is an odd amount, A wins B’s coin. If the sum is even B wins A’s coin. Find the best strategy for each player and the value of the game. [4+12] 6. (a) Discuss the stationery state of the queue system. (b) If for a period of 2 hours in a day (8-10 AM) planes arrive at the aerodrome for every 20 minutes but the service time continues to remain 32 minutes, then calculate for this period i. the probability that the aerodrome is empty ii. average queue length, on the assumption that the line capacity of the aerodrome is limited to 6 planes. [4+12] 7. (a) What is lead-time? What activities occur during lead-time? (b) An item is produced at a rate of 100 units per day. The demand occurs at the rate of 60 units per day. If the set up cost is Rs 100 per set up, holding cost is Re. 0.02 per unit per day. Find the economic batch size per run and total cost per annum. [6+10] 8. State Bellman’s principle of optimality and explain by an illustrative example how it can be used to solve multistage problem with finite number of stages. [16] ?????