Define Operations Research. State applications of Operation Research.
[7 marks]Solve the following LPP using simplex method. Max Z = 15x + 6x + 9x + 2x Subject to, 2x + x + 5x + 6x ≤ 3x + x + 3x + 25x ≤ 24 7x + x ≤ 7014 x , x , x , x ≥ 0
[20 marks]State and discuss similarities and differences between Transportation problem and Assignment Problem.
[7 marks]Obtain the dual of the following primal LP problem. 1. Maximize Z = x – 2x + 3x x 1 2 subject to the constraints
[3 marks]– 2x + x + 3x = 2,123 (ii) 2x + 3x + 4x = 1123 and x , x , x ≥ 0123 2. Minimize Z = 3x – 2x + 4x x 1 2 subject to the constraints
[3 marks]3x + 5x + 4x ≥ 7,123 (ii) 6x + x + 3x ≥ 4,123 (iii) 7x – 2x – x ≤123 (iv) x – 2x + 5x ≥ 3,123
[10 marks]4x + 7x2 – 2x ≥ and x , x , x ≥ 0123
[ marks]Explain components and assumptions of Linear Programming Model in detail.
[7 marks]Discuss the fields of application for queuing theory. Explain queue discipline and its various forms.
[7 marks]Explain in detail the Hungarian method to solve an assignment problem with Page 1 of suitable example.
[3 marks]Find the initial feasible solution of the transportation problem by Vogel’s Approximation Method. DESTINATION SUPPLY ORIGIN 1 2 3 DEMAND 60 40 30 110 240
[4 marks]Solve the following assignment problem and find the minimum cost. JOBS I II III IV A 10 12 19 11 B 5 10 7 workers C 12 14 13 11 D 8 15 11 9
[8 marks]Explain with suitable examples the different costs that are involved in the inventory problems.
[7 marks]Customers arrive at a window in a bank, according to a Poisson distribution with mean 10 per hour. Service time per customer is exponential with mean 5 minutes. The space in front of the window including that for the serviced customers can accommodate a maximum of three customers. Other customers can wait outside this space. a. What is the probability that an arriving customer can go directly to the space in front of the window? b. What is the probability that an arriving customer will have to wait outside the indicated space? c. How long is an arriving customer expected to wait before being served?
[7 marks]What is Replacement? Explain the types of failures with example.
[7 marks]Amanufacturer uses Rs. 10,000 worth of an item during the year. He has estimated the ordering cost is Rs. 25 per order and carrying costs as 12.5% of average inventory value. Find the optimal order size, number of orders per year, time period per order and total cost.
[7 marks]Explain Johnson’s procedure (steps) for processing n jobs through two machines.
[7 marks]Six jobs go first over machine Iand then over machine II. The order of the completion of jobs has no significance. The following table shows the machine times in hours for six jobs and the two machines. Job J J J J J J Machine I 2 4 9 6 7 Machine II 6 7 4 3 3 11
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[3 marks]Describe the PERT/CPM network components and rules for network construction.
[7 marks]Draw a network arrow diagram for the following information concerning some project: Activity Predecessor activities A None B A C A D B,C E C F D G E H F,G Page 3 of
[3 marks]