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Code: 9F00205
Time: 3 hours
MCA II Semester Regular & Supplementary Examinations August 2014
OPERATIONS RESEARCH
(For students admitted in 2009, 2010, 2011, 2012 & 2013 only)
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Max. Marks: 60
Answer any FIVE questions
All questions carry equal marks
- (a) Discuss the importance of operations research in decision making process.
(b) Use simple method to solve the following LPP--- Content provided by FirstRanker.com ---
Maximize z= x; + 2x, subject to
— X1 + ZXZ < 8,
X1 — 2x, < 3; x;=20andx = 0.
- (a) Use two phase simplex method to minimize
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constraints x; — 3x, + 4x3 =5,
X1 — 2%, <3, 2x;—x3 = 4; x; =2 0andx >0 and x5 is unrestricted.
(b) x1 + ZXZ <12
Z = x; + x, + x3 subject to the - (a) Use duality to solve the following LPP
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Maximize Z = 2x, + x, subject to the constraints
x1+ 2x, < 10, x; +x3 < 6,
X1— X< 2, x1—2x, < 1
(b) Use dual simplex method to solve the LPP
Maximize Z = —3x; — x, subject to the constraints--- Content provided by FirstRanker.com ---
x1+ x, =21, 2x1+3x; = 2; x3,x, = 0.
X1,X2 = 0. - (a) Use Vogel's approximation method to obtain an initial basic feasible solution of the transportation problem
D E F G Available A 11 13 17 14 250 B 16 18 14 10 300 C 21 24 13 10 400
(b) What is an assignment problem and how do you interpret it as an L.P model? - (a) Find the sequence that minimizes the total elapsed time (in hours) required to complete the following tasks on two machines.
(b) Use graphic method to find the minimum elapsed total time sequence of 2 jobs and 5 machines, when we are given the following information machines.Task A B C D E F G H Machine I 2 5 4 9 6 8 7 5 Machine II 6 18 7 4 3 9 3 8 Sequence: A B C D E Job I (Time in hours): 2 1 3 4 6 Sequence: C A D E B Job II (Time in hours): 4 5 3 2 6 - (a) A firm is considering replacement of a machine, whose cost price is Rs12,200 and the scrap value Rs 200. The running (maintenance and operating) costs in Rs are found from experience to be as follows.
When should the machine be replaced? (b) The initial cost of an item is Rs 15,000 and maintenance or running costs (in Rs) for different years are given below.Year: 1 2 3 4 5 6 7 8 Running Cost: 200 500 800 1200 1800 2500 3200 4000 Year: 1 2 3 4 5 6 7 Running Cost: 2,500 3,000 4,000 5,000 6,500 8,000 10,000 - (a) Use dynamic programming to solve the following problem.
Minimize Z = y? + yZ + y3 subject to the constraints
y1+ y2+y3 =215and y;,y,,y3 =2 0.
(b) What are the essential characteristics of dynamic programming problems? - (a) What is a game in game theory? What are the properties of a game?
(b) For the game with the following pay off matrix, determine the optimum strategies and the value of the game. - (a) What are the types of inventory? Why they are-maintained? Explain the various costs related to inventory.
(b) A baking company sells cake by the pound. It makes a profit of 50 paisa a pound on every pound sold on the day it is baked: It disposes of all cakes not sold on the date it is baked; at a loss of 12 paisa a pound. If demand is known to be rectangular between 2,000 and 3,000 pounds, determine the optimum daily amount baked.
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