What is Operations Research (OR)? What are the significant features of OR? State any four application of OR.
[7 marks]An electronic company is engaged in the production of two components Cand C12 that are used in radio sets. Each unit of Ccosts the company Rs. 5 in wages and Rs.1 5 in material, while each of Ccosts the company Rs. 25 in wages and Rs. 15 in2 material. The company sells both products on one-period credit terms, but the company’s labour and material expenses must be paid in cash. The selling price of Cis Rs. 30 per unit and of Cit is Rs. 70 per unit. Because of the company’s strong12 monopoly in these components, it is assumed that the company can sell, at the prevailing prices, as many units as it produces. The company’s production capacity is, however, limited by two considerations. First, at the beginning of period 1, the company has an initial balance of Rs. 4000. Second, the company has available in each period 2000 hours of machine time and 1400 hours of assembly time. The production of each Crequires 3 hours of machine time and 2 hours of assembly time,1 whereas, the production of each Crequires 2 hours of machine time and 3 hours of2 assembly time.Formulate this problem as an LP model so as to maximize the total profit to the company.(DO NOT SOLVE)
[7 marks]Construct the dual of the problem. Max z = 6x + 4x + 6x + x subject to the constraints
[7 marks]4x + 4x + 4x + 8x = (ii) 3x + 17x + 80x +2x ≤ 48 Where x , x ≥ 0 and x , x are unrestricted.
[ marks]Solve the following LP problem using Simplex method: Maximize Z = x − x + 3x123 subject to the constraints x + x + x ≤10123 2x − x ≤ 213 2x − 2x + 3x ≤ 0123 and x , x , x ≥ 0.123
[7 marks]Use penalty (Big-M) method to solve the following LPP Maximize Z = 2x +4x12 Subject to 2x + x ≤1812 3x +2x ≥ 3012 x + 2 x = 26 and x , x ≥ 0.
[7 marks]Solve the following assignment problem: A 41 72 39 52 25 B 22 29 49 65 81 C 27 39 60 51 40 D 45 50 48 52 37 E 29 40 45 26 30 Minimize the total cost.
[7 marks]07 Determine an initial basic feasible solution to the following transportation problem using (i) Least Cost Method and (ii) Vogel’s Approximation Method: Destinations Origins Availability D D D D O 5 3 6 21 19 O 4 7 9 1 372 O 3 4 7 5 343 Demand 16 18 31 25 90
[ marks]Define: Simulation. State the advantages and disadvantages of simulation.
[7 marks]Define: Two- person zero- sum game, Saddle point.For the game with payoff matrix: Player B Player A B1 B2 B3 B4 A1 3 −5 0 A2 −4 −2 1 A3 5 4 2 Determine the best strategies for players Aand Band th e value of the game. Is this game (i) fair? (ii) strictly determinable?
[3 marks]Arrivals at a telephone booth are considered to be Poisson, with an average time of minutes between one arrival and the next. The length of a phone call is assumed to be d istributed exponentially, with mean 3 minutes. Find: 1. The probability that an arrival finds that four persons are waiting for their turn. 2. The average number of persons waiting and making telephone calls. 3. The average length of the queue that is formed time to time.
[7 marks]Describe the characteristics of Calling Population (input source) of a Queuing System. What do you understand by Queue Discipline?
[7 marks]The data collected in running a machine, the cost of which is Rs. 60,000 are given below: Year 1 2 3 4 Resale value (Rs) 42,000 30,000 20,400 14,400 9,650 Cost of spares (Rs.) 4,000 4,270 4,880 5,700 6,800 Cost of labour (Rs.) 14,000 16,000 18,000 21,000 25,000 Determine the optimum period of replacement of the machine.2
[5 marks]An engineering company is offered a material handling equipment A. It is priced at Rs. 60,000 including cost of installation. The costs for operation and maintenance are estimated to be Rs. 10,000 for each of the first five years, increasing every year by Rs. 3,000 in the sixth and subsequent years. The company expects a return of 10% on all its investment. What is the optimal replacement period?
[7 marks]Explain different type of Inventory Cost.
[7 marks]precedence relationships of the activities, and activity time estimates of a project is as follows Task A B C D E F G H I J Precedence - A - C B,C C F D,E,G D,E H,I Time 10 5 15 11 10 5 5 10 10 1. Draw the network of the project. 2. Obtain the total, free and independent float values for non-critical activities.
[15 marks]Amachine operator has to perform three operations, turning, threading 07 and knurling on a number of different jobs. The time required to perform these operations (in minutes) for each job is known and is given below: Time Job Time for Time for for turning threading knurling Determine the order in which the jobs should be processed in order to minimize the total time required to turn out all the jobs.
[7 marks]Explain the difference between PERT and CPM.
[7 marks]