What is Operations Research? Briefly explain the Applications of OR in various fields.
[7 marks]Solve using the Graphical method the following problem: Maximize Z = 3x + 2y subject to: 2x + y ≤ 18 2x + 3y ≤ 42 3x + y ≤ 24 x ≥ 0 , y ≥ 0
[7 marks]Solve using the simple method: Maximize z = 3x1 + 2x2 subject to -x1 + 2x2 ≤ 3x1 + 2x2 ≤ x1 – x2 ≤ x1, x2 ≥ 0
[3 marks]Solve the following LPP using Big M Method. Minimize Z = 3x1 + x2 Subject to constraints 4x1 + x2 = 4 ....................(i) 5x1 + 3x2≥ 7 ....................(ii) 3x1 + 2x2≤ 6 ....................(iii) Where x1 , x2≥0.
[7 marks]What is linear programming? Give the mathematical model of linear programming problem. Briefly explain with an example.
[7 marks]Describe the characteristics of calling population (input source) of a queuing System. What do you understand by Queue discipline?
[7 marks]Determine an initial Basic feasible solution to the following Transportation Problem by using (a) Least Cost Method (b)Vogel Approximation Method. D1 D2 D3 D4 Supply S1 11 13 17 14 250 S2 16 18 14 10 300 S3 21 24 13 10 400 Demand 200 225 275 2501
[7 marks]Explain Errors and Dummies in network diagram with suitable figure.
[7 marks]What do you mean by unbalanced transportation problem and unbalanced assignment problem? How can you convert them into balanced problem?
[7 marks]Acompany makes bicycles. It produces 450 bicycles a month. It buys the tires for bicycles from a supplier at a cost of $20 per tire. The company’s inventory carrying cost is estimated to be 15% of cost and the ordering is $50 per order. a.Calculate the EOQ b.What is the number of orders per year? c.Compute the average annual ordering cost. d.Compute the average inventory. e.What is the average annual carrying cost? f.Compute the total cost.
[7 marks]Define simulation. Explain various stages involved in simulation process.
[7 marks]Write the mathematical form of transportation. Represent assignment problem as a special case of transportation problem.
[7 marks]Discuss the various costs involved in an inventory model.
[7 marks]Amill owner finds from his past records the costs of running a machine whose purchase price is Rs.6000 are as given below Year 1 2 3 4 5 6 Running cost(Rs) 1000 1200 1400 1800 2300 2800 3400 Resale value (Rs) 3000 1500 750 375 200 200 200 Determine at what age is a replacement due?
[7 marks]Explain its advantages and disadvantages of simulation.
[7 marks](1) Define the following terms:
[7 marks]Payoff matrix (ii) saddle point (iii) two-person zero-sum game (iv) competitive game
[ marks]Briefly Explain the structure of Queuing system.
[7 marks]