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

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Total No. of Questions : 12] P1021 [Total No. of Pages :5 [3864] - 106 B.E. (Civil) SYSTEMS APPROACH IN CIVIL ENGINEERING (1997 & 2003 Course) (Elective - I) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer three questions from Section - I and three 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) Fiqures 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) b) Minimize Z = x1 + x2 + 3x3 S.t 3x1 + 2x2 + x3 3 2x1 + x2 + 2x3 2 x1, x2, x3 0 Use Big M Method. [12] What is an infeasible solution? [4] OR Q2) a) b) Solve the problem in Q1(a) above using Two - Phase Method. What are slack variables and artificial variables? [12] [4] Q3) The unit cost of transporting construction material from three sources to four construction sites is given below, along with the availability at each source and the requirement at each site. [18] a) Find the Initial Feasible solution by i) N-W Corner Method ii) VAM P.T.O. Source Sites Supply B C D 1 25 17 25 14 300 2 15 10 18 24 500 3 16 20 8 13 600 Demand 300 b) A 300 500 500 Using the solution obtained by VAM, find the distribution policy which will minimize the cost of transportation. OR Q4) a) Five contractors have submitted their proposals for executing four projects. The likely profits to be earned by each contractor for each of the projects is given below. If one project is to be allocated to one contractor only [10] i) Find the optimal allocation that will maximize profits. ii) Find the maximum value of the profits. Contractor [2] Projects 1 2 3 4 A 62 71 87 48 B 78 84 92 64 C 50 61 111 87 D 101 73 71 77 E 82 59 81 80 b) Explain when degeneracy occurs in a Transportation problem. c) Explain how a transportation model is a Linear programming model. [4] Q5) a) Use Fibonacci method to find the minimum value of the function 128 , in the range 0 to 10, to an accuracy of 0.5%. Carry out x computations for the first four stages only. [10] Explain local and global optima. [6] Z = x2 + b) [2] OR [3864]-106 -2- Q6) a) b) 2 2 Use Newton s method to maximize f (x) = 9x1 x1 + 8x2 2x2 Take the starting point as (0, 0) Explain the algorithm of steepest Gradient Method. [10] [6] SECTION - II Q7) a) b) Use Lagrange Multiplier Technique to minimize [6] 2 2 Z = x1 + 2x2 + 3x1 + 7x2 . subject to x1 + x2 = 5 Equipment is to be transported from destination X to destination Y. Various routes are available for this transport. The travel distances along various routes, between nodes is given below, in Km. Use dynamic programming to determine the shortest route between X and Y. [12] From X X X X A A B B C C D D E E F F F G G H I J K [3864]-106 To A B C D E F E G F G F G I J H I K I J Y Y Y Y Distance 9 7 13 14 11 5 7 11 12 1 5 8 2 14 7 3 14 14 8 15 5 9 1 OR -3- Q8) a) b) Solve the problem given in Q7(a) above using Dynamic Programming.[12] Explain Forward Recursion and Backward Recursion. [6] Q9) a) Find the sequence that minimizes the total time required for performing the following jobs on three machines in the order A-B-C. [10] Job Processing Times in Minutes. A C 1 8 3 8 2 3 4 7 3 7 5 6 4 2 2 9 5 5 1 10 6 b) B 1 6 9 Find the total elapsed time and idle times of machines B & C Explain the various components of a Queue and their characteristics.[6] OR Q10)The inter arrival time and the service time in a waiting line model have the following frequency distribution based on 100 such arrivals. [16] Inter arrival time in minutes 1 2 3 4 5 6 7 Frequency 4 10 13 22 30 14 7 Service time in minutes 1 2 3 4 5 6 Frequency 3 8 25 39 16 9 Estimate the average customer waiting time and the percentage waiting time, average idle time and percentage idle time of the service facility and the average queue length by simulating 10 arrivals. Use the following random numbers. Arrivals : 23, 58, 56, 44, 80, 36, 97, 26, 71, 62, Service : 60, 21, 68, 76, 52, 08, 25, 84, 38, 05 [3864]-106 -4- Q11)a) Explain the assumptions in a Two -Person - Zero Sum Game. [3] b) Explain the theory of Dominance. [3] c) The payoff matrix in a game between A and B is as follows. Determine the strategies of each player and the value of the game. The payoffs are for player A. [10] B1 B2 B3 B4 B5 A1 3 2 2 0 6 A2 4 2 1 7 4 A3 2 5 4 1 1 A4 0 3 3 1 1 OR Q12)a) b) What are the factors affecting the choice of a project from amongst various alternatives. [6] Following data pertains to two projects. Particulars [10] Project A Project B Investment in Rs. lakh. 50 58 Useful life in years 15 12 Annual Benefits in Rs. lakh 10 12 10% 10% Discount Rate Discuss the choice of the projects based on NPV and B/C ratio. Rank the projects. kbkb [3864]-106 -5-

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Additional Info : 2003 & 1997 Course
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