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PUNJAB TECHNICAL UNIVERSITY MCA - II (SEM 3) SEP 2010 : Computer Based Optimisation Methods

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Roll No. ...................... Total No. of Questions : 13] [Total No. of Pages : 04 Paper ID [A0515] (Please fill this Paper ID in OMR Sheet) MCA (305) (S05) (O) (LE) (Sem. - 3rd) COMPUTER BASED OPTIMISATION METHODS Time : 03 Hours Maximum Marks : 75 Instruction to Candidates: 1) Section - A is Compulsory. 2) Attempt any Nine questions from Section - B. Q1) Section - A (15 2 = 30) a) What are characteristics of OR? b) What is convex set? c) How the models in OR be classified? d) How OR is useful in decision making? e) What is duality in LP? f) What are loops in transportation problem? g) How is transportation problem formulated? h) What is the mathematical formulation of assignment problem? i) What is traveling salesperson s problem? j) What are unbalanced transport problems? k) Define conditional probability. l) What is decision making under uncertainty? m) Define integer programming. n) o) A-533 What is branch-and-bound method? What is dynamic problem? P.T.O. Section - B Q2) (9 5 = 45) Explain the problem solving using simplex method through an appropriate example. Q3) Find the graphical solution for the following problem : Maximize z = 3xl + 4x2 s.t. 4xl + 2x2 < = 80 2xl + 5x2 < = 180 xl, x2 > = 0 Q4) Find basic feasible solution to the following LPP : Maximize z = 2xl+ 3x2+4x3+ 7x4 s.t. 2xl + 3x2 x3 + 4x4 = 8 xl 2x2 + 6x3 7x4 = 3 xl, x2, x3, x4 > = 0 Q5) Use duality to solve the following LPP Maximize z = 2x1 + x2 s.t. xl + 2x2 < =10, xl + x2 < = 6 xl x2 <= 2, xl 2x2 <= 1, xl, x2 > = 0 Q6) Consider the following transportation table showing production and transportation costs, along with the supply and demand position of the factories : M1 M2 M3 M4 Supply F1 4 6 8 13 500 F2 13 11 10 8 700 F3 14 4 10 13 300 F4 9 11 13 3 500 Demand 250 350 1050 299 Obtain an initial basic feasible solution by using VAM. Find out an optimal solution for the even given problem. Q7) Explain N- W corner method with example. A-533 2 Q8) A departmental head has four subordinates, and four tasks to be performed. The subordinates differ in efficiency, and the tasks differ in their instrinsic difficulty. His estimate for time each man would take to perform each task, is given below : Men Tasks E F G H A 18 26 17 11 B 13 28 14 26 C 38 19 18 15 D 19 26 24 10 How should the tasks be allocated, one to a man, so as to minimize the total man-hours? Q9) A firm having two sources S1 and S2 wishes to ship its products to two destinations D1 and D2, the number of units available at S1 and S2 are 5 and 25 respectively and the product demanded at D1 and D2 are 20 and 10 units respectively. The firm, instead of shipping directly from sources to destinations decides to investigate possibility of transshipment. The unit transportation costs (in rupees) are given in the following table. Find the optimal shipping schedule : source Destination S1 S2 D1 D2 Demand Source 0 2 2 0 3 2 4 4 ----- ----- : : : : : Destination 3 4 2 4 0 1 1 0 20 10 Available 5 25 ---------- Q10) A businessman has three alternatives open to him each of which can be followed by any of the four possible events, The conditional payoff (in Rs.) for each of the event is given below : Alternative X Y Z Payoffs conditional on events A B C 8 0 -10 4 12 18 14 6 0 D 6 -2 8 Determine which alternative should the businessman choose, if he adopts the maximum criterion. A-533 3 Q11) From a bag containing 10 black and 5 white balls, a ball is drawn at random. What is the probability that it is white? Q12) Divide a positive quantity in such a way that their product is maximum. Q13) Solve the following problem by branch and bound technique. Max. z = x1 + x2 s.t. 3xl + 2x2 <= 12 x2 < = 2, x1, x2 > = 0 and both are integers. kbkb A-533 4

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Additional Info : Mca - II (sem 3) September 2010 Question Paper - Computer Based Optimisation Methods
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