Quantitative Technique

What is a linear programming paradox? talk of the scope and role of linear programming in make counseling chores. converse and describe the role of linear programming in managerial decision-making bringing out limitations, if any. 2. condone the concept and computational steps of the unidirectional method for solving linear programming problems. How would you identify whether an optimal termination to a problem obtained employ simplex algorithm is unique or not? a)What is the difference between a executable solution, a basal feasible solution, and an optimal solution of a linear programming problem? )What is the difference between simplex solution procedure for a maximation and a minimisation problem? c)Using the concept of net contribution, provide an primordial explanation of why the criterion for optimality for maximization problem is different from that of minimization problems. Outline the steps involved in the simplex algorithm for solving a linear programming ma ximization problem. Also define the good terms used therein. 3. Linear programming is one of the most oftentimes and successfully employed Operations Research proficiencys to managerial and business decisions. separate this statement with some examples. 2 2 4. soak up the transporation problem and wee its mathematical perplex. apologize, by taking an illustration, the North-West Corner Rule, the Least constitute Method and the Vogels Approximation Method to obtain the sign feasible solution to a transportation problem. Discuss the various methods of finding initial feasible solution of a transportation problem and state the advantages, disadvantages, and areas of employment for them. 5. What is an assignment problem? It is true to say that it is a special grimace of the transportation problem?Explain. How ignore you formulate an assignment problem as a standard linear programming problem? Illustrate. What do you recognise by an assignment problem? thrust a brief syn opsis for solving it. 6. What are different suits of inventories? Explain. What functions does inventory perform? State the deuce basic inventory decisions management must make as they tone-beginning to accomplish the functions of inventory just described by you. 7. What is queuing guess? What type of questions are sought to be answered in analyzing a queuing governance? Give a general structure of the queuing system and apologize.Illustrate some queuing situations. What is queuing speculation? In what types of problem situations can it be applied successfully? Discuss giving examples. 8. What is a electrical switch problem? observe some all important(p) replacement situations and policies. Briefly explain the costs which are relevant to decisions for replacement of depreciable assets. Illustrate their behaviour and explain how the optimal time for replacement of an asset can be determined. 3 3 9. What kinds of decision-making situations may be analysed using sassy and CP M techniques? State the major similarities between PERT and CPM.Under what good deal is CPM a better technique of exteriorise management than PERT? A construction club has received a contract to build an chest complex. It has frequently engaged itself in constructing such buildings. Which of the two network techniques, PERT and CPM, should in your opinion, be employed by the company? Why? 10. Describe the steps involved in the process of decision making. What are pay-off and distress functions? How can entries in a regret table be derived from a pay-off table? 11. What do you understand by Markov processes? In what areas of management can they be applied successfully?What do you understand by diversity probabilities? Is the assumption of stationary transition probabilities realistic, in your opinion? Why or why not? 12. Explain how the probability tree helps to understand the problem of Markov processes. Explain the method of calculation of ending up in distributively absorb ing state when a chain beings in a picky transient state. What is fundamental matrix of Markov chains? What does it calculate? 13. What is simulation? Describe the simulation process. State the major two reasons for using simulation to solve a problem. What are the advantages and limitations of simulation? When it becomes difficult to use an optimization technique for solving a problem, one has to resort to simulation. Discuss. Simulation is typically the process of carrying out sampling experiments on the models of the system rather than the system itself. Elucidate this statement by taking some examples. 4 4 14. A company has three offers for its existing equipment in one of the divisions. The outgrowth buyer is willing to pay Rs. 50,000 at the end of 8 eld period. The second buyer offers Rs. 39,000consisting of an immediate payment of Rs. 14,000 and Rs. 25,000 after 6 years.The trinity buyer agrees to buy the equipment for Rs. 29,000 payable right away. Which is the best off er for the company if it can earn an interest 8% per annum on the money received? 15. What is the difference between qualitative and quantitative techniques of forecasting. When is a qualitative model appropriate? Briefly discuss the Delphi method of making forecasts. 16. a)How do you refer between resource leveling and resource allocation problems? State and explain an algorithm for resource allocation. b)Explain the following as they are used in PERT/CPM (i)Beta distribution, and (ii) Budget over-run. 5 5 17.The following table come backs info on normal time and cost, and crash time and cost for a project. Duration (Weeks)Total Cost (Rs) Activity NormalCrashNormalCrash 1 232300450 2 333 75 75 2 453200300 2 544120120 3 441100190 4 632 90130 5 6 31 60110 i)Draw the network and find out the critical path and the normal project age. ii)Find out the total float associated with each activity. iii)If the indirect costs are Rs. 100 per week, find out the optimum duration by cr ashing and the identical project costs. iv)With the crash duration indicated, what would be the minimum crash duration possible, ignoring indirect costs? 8. What is a game in game theory? What are the properties of a game? Explain the best strategy on the basis of minimax criterion of optimality. Describe the maximin and minimax principles of game theory. 6 6 19. Explain the steps involved in solution to dynamic programming problems. Explain the following in the context of dynamic programming (a)Stages (b)States (c)Pay-off function (d)Recursive relationship 20. A political campaign for election to the parliament is entering its final examination stage and pre-poll surveys are medicating a very close contest in a certain constituency.One of the candidates in the constituency has sufficient funds to give five full-page advertisements in four different areas. Based on the polling information, an estimate has been made of the approximate build (in thousands) of additional votes that can be polled in different areas. This is shown below. No. ofArea Commercial AdsABCD 0 0 0 0 0 1913117 21517115 31212325 425232129 531252733 Using dynamic programming, determine how the five technical ads be distributed between the four areas so as to maximize the estimated number of votes.