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Linear Programming: 1. What are the essential characteristics of a linear programming model? 2. Explain the terms: key decision, objective, alternatives and restrictions in the context of linear optimization models by assuming a suitable industrial situation. 3. Explain important characteristics of the industrial situations to which linear programming method can be successfully applied. Illustrate applications of this technique with a suitable example. 4. Explain the terminologies of linear programming model. 5. List and explain the assumptions of linear programming problems. 6. Define the following. (a) Alternate Optimum solution (b) Unbounded solution (c) Infeasible solution (d) Degenerate solution (e) Slack variable (f) Surplus Variable (g) Artificial variable (h) Basic variable (i) Criterion Value Transportation Problem: 1. Give different practical applications of transportation problem. 2. What are types of transportation problem? Explain them with suitable examples. 3. Write a linear programming model of the transportation problem. 4. Write the procedure for each of the following (a) Northwest- corner cell method (b) Least cost cell method (c) Vogel’s approximations method (d) U-V method. Assignment Problem: 1. Discuss the similarity between transportations problem and assignment problem. 2. Discuss practical applications of assignment problem. 3. Develop a zero-one programming model for assignment problem. 4. Discuss the steps of Hungerian method. Network Techniques: 1. What is the shortest path problem? Give some practical applications of the shortest path problem. 2. What is minimum spanning problem? What are its practical applications? 3. State maximal flow problem and give its practical applications 4. Explain the steps of the following algorithms (a) Dijikstra’s algorithm, (b) Floyd’s algorithm (c) PRIM algorithm (d) Kruskal’s algorithm Queueing Theory: 1. Discuss the application areas of queueing theory 2. List and explain the terminologies used in queueing system 3. What is Kendall notation? Give the classification of queueing system based on Kendall notation. 4. The arrival rate of customers at a banking counter follows Poisson distribution with a mean of 30 per hour. The service rate of the counter clerk also follow Poisson distribution with a mean of 45 per hour. (a) What is the probability of having 0 customer in the system (p0)? (b) What is the probability of having 8 customer in the system (p8)? (c) What is the probability of having 12 customer in the system (p12)? (d) Find Ls, Lq, Wq and Ws. 5. Vehicles are passing through a toll gate at the rate of 70 per hour. The average time to pass through the gate is 45 seconds. The arrival rate and service rate follow Poisson distribution. Three is a complaint that the vehicles wait for long duration. The authorities are willing to install on more gate to reduce the average time to pass through the toll gate to 35 seconds if the idle time of the toll gate is less the 9% and the average queue length at the gate is more than 8 vehicles. Check whether the installation of the second gate is justified.
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