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You are here:Open notes-->VTU-->Sixth-Semester-BE-Degree-Examination-JuneJuly-2013-Operations-Research-Question-paper

Sixth Semester B.E. Degree Examination, June/July 2013 Operations Research Question paper

USN 10CSIIS661 Sixth Semester B.E. Degree Examination, June/July 2013 Operations Research Time: 3 hrs. Max. Marks: 100 Note:Answer FWEfuli questions, selecting at least TWO questions from each part.


1),a.Define operations research. List and explain the various phases of an operations research (08 Marks)

b. A,farmer has to plant two kinds of trees P and Q in a land of 400m2 area. Each P tree requires.at least 25m2 and Q tree requires 40m2 of land. The annual water requirement of P tree is 30Junits and of Q tree is 15 units per tree, while at month;(3,OOOunits of water is available It is also estimated that the ratio of the number of Q tree'\ to the number of P trees should not be less than 6119 and should not be more than 17/S. Then return per tree from P is expected to be one and half times as much as from Q tree.evaluvate the problem as an LPP model. (06 Marks)

C.2solve the following LPP@ Subject to the constraints ';/~ .X22 3, ACf,~" x, x~2 ,,\ And 5-0 '-J Xl, X2- . \:

2) a. Defme basic solution and obtain equations: 2Xl + 3X2+ 4X3= 10, ~ 3Xl + 4X2+ X3= 12 O~ , Also, classify the solutiQR~to

i) Basic feasible solution~n ~~~ Degenerate~ ~afc solution . . . 111) Non-degenerate feasible solution.

b. Solve the foll 10 \ ~ - , ~'\ X2220, ~' X3230 "I. ~ and xi, X2,X320. (06 Marks)

C. Solve the following LPP by two-phase simplex method: Maximize Z = 3Xl - X2 Subject to the constraints 2Xl + X22 2, x, + 3X2::;2, X2::;4 and xr, X22 0. (10 Marks) lof3 ~RT,-

3) a. Write any five key relationships be ' he primal and the dual problems.

b. Write the duals of the following L i) Maximize Z = 7xI + 4X2 Subject to the constraint 2xI - X3S; 10, 2 + X3S; 6 XI, X2,X3:2: O. ii) I + 2X2+ X3 constraints 2xI - 3X2+ X3S; 5, 4xI - 2X2 :2: 9, -Sx, + 4X2+ 3X3= 8 a XI, X2:2: 0 and X3is unrestricted.

c. :1 the following LPP by dual simplex method: inimize Z = 2xI + 2X2+ 4X3 Subject to the constraints 2xI + 3X2+ 5X3:2: 2, 3xI + X2+7X3 S; 3, XI + 4X2+ 6X3 S; 5 and XI, X2,X3:2: O. b. Solve the following LPP by Big-M method: Maximize Z = -Zx, - X2 Subject to the constraints 3xI + X2= 3, 4xI + 3X2 :2: 6, XI + 2X2 S; 4 and Xl, X2:2: O.

4) a. aoJve the following LPP by revised simplex method: M~ . ize Z = 2xI + X2 Sub the constraints 3xI + 4X2 S; 6, t X2S; 3 And 2:2: 0 b. Explain the fol i) Weak dualit perty ii) Strong duality p erty iii) Complementary solW' ns property iv) Complementary opti lutions prop

Part B

6) a. A company has 3 cement factories located in 3 cities X, Y and Z which supply cement to 4 project sites located in cities A, B, C and D. Each plant can supply 6, 1 and 10 truckloads of cement daily and the daily requirements of the projects are 7, 5, 3 and 2 truckloads respectively. The transportation cost (in thousands of rupees) per truck load of cement from each plant to each project site are shown below. 20f3 Projects ABC D 2 3 11 7 1 0 6 1 5 8 15 9 10CS/IS661 X Plants y Z _:":>_ . ~~,'C\~~f '""-"''''i~ Determine the optimal distribution of the company so as to minimize the total transPQit'afi~n cost. Use V AM method to find the initial BFS. ;!r~2)\Iarks) Solve the following assignment problem: \:c~ Machines MJ M2 M3 M4 J1 11 17 8 16 h 9 7 12 6 Jobs h 13 16 15 12 h 21 24 17 28 J5 14 19 12 11 7 a. Define the following with i) Pay-off ii) Zero-sum game iii) Saddle point. b. Solve the following game by Dorni rinciple: II Player A AI 3 2 ' A2 3 4 A3 4 2 ~ 0 4 ing game by graphical method: Player B BI B2 B3 B4 Player A AI CIIII=II}] A2~ Write a short note on decision trees.;~. (08 Marks) (03 Marks) (06 Marks) 07 Marks) (9"J>:\arks)


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