K L University 2009 B.Tech Information Technology Model Operations Research, IT 323 - Question Paper

KONERU LAKSHMAIAH COLLEGE OF ENGINEERING (AUTONOMOUS)
DEPARTMENT OF info SCIENCE AND TECHNOLOGY
MODEL ques. PAPER
III/IV B.TECH exam

Academic Year: 2008-2009 Semester: II
Subject: Operations Research Code: IT 323
Duration: three Hours Max.Marks:60

UNIT-I

1. a) describe Generalized linear programming issue. Old hens can be bought for Rs.2.00 every but young ones cost Rs.5.00 every. The old hens can lay three eggs per week and the young ones, five eggs per week, every being worth of 30 paise. A hen costs Re.1.00 per week to feed. If I have only Rs.80.00 to spend for hens, how many of every type should I buy to provide a profit of more than Rs.6.00 per week, assuming that I cannot house more than 20 hens? Write a mathematical model for the issue. (2 + 4)Marks
b) Solve the subsequent LPP graphically :Maximize Z = 50X1 + 60X2, subject to the constraints 2X1 + 3X2 = 1500, 3X1 + 2X2 = 1500, 0 =X1 = 400, and 0 =X2 = 400. six Marks
(OR)
2. Solve the LPP by using Simplex method: Maximize Z = 3X1 + 2X2 + 5X3 subject to the constraints X1 + 2X2 + X3 = 430, 3X1 + 2X3 = 460, X1 + 4X2 = 420, and X1=0, X2=0. 12 Marks

UNIT-II

3. a) provide Mathematical formulation of transportation issue. 4Marks
b) obtain the optimum (minimum) solution to the subsequent transportation issue through Vogel’s Approximation method 8Marks
D1 D2 D3 D4 Supply
F1 11 13 17 14 250
F2 16 18 14 10 300
F3 21 24 13 10 400
Demand 200 225 275 250

(OR)
4. Explain the graphical method of solving (2 x n) and (m x 2) games. Solve the game graphically, whose payoff matrix to the player A is provided by
Player B
Player A 12 Marks
UNIT-III

5. a) discuss clearly the different costs that are involved in inventory issues with suitable examples. 6Marks
b) The demand for an item in a company is 18,000 units per year and the company can produce the item at a rate of 3,000 units per month. The cost of 1 set up is Rs.500.00, holding cost of 1 unit per month is 15 paise, and the shortage cost is Rs.20.00 per month, per unit item. Then determine the following: (i) optimum production batch volume and the number of shortages. (ii) optimum cycle time and production time. (iii) maximum inventory level in the cycle. (iv) the total associated cost per year if the cost of the item is Rs.20.00 per unit. 6Marks
(OR)
6. a) What is ‘ABC’ analysis? elaborate the basic steps in implementing it? 6Marks
b) Perform ABC analysis on the subsequent sample of items in an inventory6Marks
Model Number Annual Consumption in pieces Unit Price (in Paises)
501 30,000 10
502 2,80,000 15
503 3,000 10
504 1,10,000 5
505 4,000 5
506 2,20,000 10
507 15,000 5
508 80,000 5
509 60,000 15
510 8,000 10

UNIT-IV
7. a) discuss the subsequent terms in the contest of PERT
(i) Normal time (ii) Optimistic time (iii) Pessimistic time (iv) Variance and estimated time of an activity 6Marks
b) describe network diagram. discuss briefly the Fulerson’s rules of drawing network diagram 6Marks
(OR)
8. a) Distinguish ranging from CPM and PERT. 6Marks
b) The subsequent table provide the activities in the construction of a project and their time estimates (in days).
Activity Optimistic Time Most likely Time Pessimistic Time
1-2 3 6 15
1-6 2 5 14
2-3 6 12 30
2-4 2 5 8
3-5 5 11 17
4-5 3 6 15
5-8 1 4 7
6-7 3 9 27
7-8 4 19 28
(i) Draw the project network
(ii) compute length and variance of the critical path
(iii) What is the approximate probability that the jobs on the critical path will be completed in 46 days? 6Marks

UNIT-V
9. State Bellman’s principle of optimality. Solve the subsequent dynamic programming issue. Maximize Z = Y1.Y2.Y3, subject to constraint: Y1+Y2+Y3=5, and Y1, Y2, Y3 =0. 12Marks
(OR)
10. a) describe simulation model. Distinguish ranging from the deterministic and stochastic simulation models. 6Marks
b) discuss Monte-Carlo simulation. 6Marks

Earning:   Approval pending.