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Systems Approach in Civil Engineering (Elective I) (April 2010)

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Total No. of Questions : 12] [Total No. of Pages : 4 [3764]-106 P1300 B.E. (Civil) SYSTEMS APPROACH IN CIVIL ENGINEERING (2003 & 1997 Course) (Elective - I) Time : 3 Hours] [Max. Marks : 100 Instructions to candidates : 1) Answer 3 questions from Section I and 3 questions from Section II. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) Solve using Big M or Two - Phase Method, [12] Maximize Z = 2x1 + 3x2 Subject to x1 6 x1 + 2x2 10 x1 + x2 2 x1, x2 0 b) Explain convex and concave functions. [4] OR Q2) a) Solve the problem in Q1(a) above by graphical method. [6] b) Explain the role of artificial variables and decision variables in L.P. [6] c) What are the applications of L.P. in Civil Engineering. [4] Q3) Solve the following Transportation problem in which the quantity available at the source, the demand at the destination and the unit cost of transportation are given in the following table. [18] a) Find the initial basic feasible solution by N-W Corner method and Least cost method. P.T.O. b) Using the solution obtained by LCM, find the optimal solution. Source Destination Supply 1 2 3 4 A 21 16 25 13 11 B 17 18 14 23 13 C 32 27 18 41 19 Demand 6 10 12 15 OR Q4) a) How will you formulate a Transportation problem as an L.P model? [6] b) Explain how you will solve an assignment problem where a particular assignment is restricted? How will you maximize the objective function in an Assignment Model. [4] c) A company has four machines on which three jobs have to be done. Each job can be assigned to one and only one machine. The cost of each job on each machine is given below. What are the job assignments which will minimize the cost? [8] Jobs Machines 1 2 3 4 A 18 24 28 32 B 8 13 17 19 C 10 15 19 22 Q5) a) Explain Dichotomous search technique for one dimensional optimization problems. [6] b) Use the golden section method to minimize Z = 2x2 16x in the range of 0 to 10. Carry out the first four iterations only. [10] OR Q6) a) Use steepest gradient technique to maximize 2 2 f(x) = 6 x1 + 4 x2 2 x1 2 x1 x 2 2 x 2 . Take the starting point as (1, 1). Carry out the first two iterations only. [10] b) [3764]-106 Explain the algorithm of Newton s method. What are its advantages over steepest gradient technique? [6] 2 SECTION - II Q7) a) b) Explain the algorithm of Lagrange Multiplier Technique. [6] 2 2 Use Lagrange Multiplier Technique to minimize = x1 + x2 2 x 2 + 1 2 subject to x12 + x2 = 4 , x1, x2 0. [10] OR Q8) a) A promoter builder has 3 money units which he wishes to utilize in developing 3 projects. Depending upon the amount invested, the resulting profits expected are given below. Determine the optimal allocation to each of the projects which will maximize the total expected returns. [12] Investment Projects 1 0 0 0 1 4 2 6 2 8 10 10 3 Q9) a) 3 0 b) 2 12 12 12 What is Bellman s principle of optimality? [4] Vehicles arrive at a service station in a Poisson fashion at an average rate of 45 minutes. The average time taken for service is 30 minutes with an exponential distribution. [10] Determine: i) The chance that a vehicle will be serviced straight away. ii) The proportion of time the service station is busy. iii) The average number of vehicles in the queue and the system. iv) The average time spent by the vehicle waiting in the queue and the system. v) The probability that there are two vehicles in the queue. b) Explain the Monte Carlo method of simulation. c) Give any two applications of simulation in the field of Civil Engineering. [4] OR [3764]-106 3 [4] Q10)a) b) Explain in brief the various components of a queueing system. What is Kendell - Lee Notation? [6] A company has 6 jobs which are to be processed on 3 machines A, B & C in the order ABC. The processing time in minutes for each job on each machine is as given below. Find the optimal sequence of the jobs so as to minimize the total time elapsed. Also find the idle time on each machine. [12] Jobs 1 2 3 4 5 6 Machines A B C Q11)a) b) Q12)a) b) c) 36 14 38 24 24 24 58 22 46 Explain the following terms: i) Two person zero-sum game. ii) Pure strategy. iii) Mixed strategy. iv) Minimax and maximin principle. 86 12 56 74 24 72 [8] Solve the following game whose payoff matrix is given in the following table. [8] Player A Player B B1 B2 B3 A1 11 17 12 A2 16 12 17 A3 15 12 16 Determine the strategies of each player and the resulting payoff. OR What criteria are considered for selection of a project amongst various alternatives available? [6] Distinguish between mutually compatible projects and mutually exclusive projects. [4] Explain the following terms: [6] i) Amortization. ii) Salvage value. iii) Discount Rate. Y [3764]-106 72 4 94 4

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Additional Info : April 2010 Examination - Systems Approach in Civil Engineering (Elective I) (2003 & 1997 Course)
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