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business
understanding management

Questions and Answers of Understanding Management

15. The payoff is the variable of interest in a dynamic programming problem. Mark the statements as T (True) or F (False).
14. All dynamic programming problems call for maximising the given payoff function. Mark the statements as T (True) or F (False).
13. The states of a given stage refer to the various possible conditions in which the system can be in that stage. Mark the statements as T (True) or F (False).
12. Every stage in a dynamic programming problem calls for making a policy decision. Mark the statements as T (True) or F (False).
11. Each sub-problem in a dynamic programming problem is called a stage. Mark the statements as T (True) or F (False).
10. Probabilistic dynamic programming is used where it is not possible to break the given problem into clear cut sub-problems. Mark the statements as T (True) or F (False).
9. In a shortest route problem, the optimal solution indicates the length of most direct route from origin to destination that involves least number of nodes on the route. Mark the statements as T
8. Dynamic programming is similar to linear programming in its approach to solving problems. Mark the statements as T (True) or F (False).
7. In dynamic programming, there is a standard algorithm which can be programmed to solve all problems. Mark the statements as T (True) or F (False).
6. BY dynamic programming it is possible to obtain the best and next-best solution to a problem. Mark the statements as T (True) or F (False).
5. The optimal solution to a dynamic programming problem is obtained by solving all stages of the problem sequentiallY. Mark the statements as T (True) or F (False).
4. Dynamic programming problems consist of a series of independent sub-problems. Mark the statements as T (True) or F (False).
3. In dynamic programming, the given problem is solved in stages beginning at the last stage and working backward to initial stage. Mark the statements as T (True) or F (False).
2. A dynamic programming problem consists of multiple smaller problems, known as states, with interconnected decisions.Mark the statements as T (True) or F (False).
1. Dynamic programming is a quantitative analysis technique which is applied to large, complex problems. Mark the statements as T (True) or F (False).
An investor has Rs 10,000 to invest and she has an opportunity to invest the amount in either of two investments A or B, at the beginning of each of the following three years. The investment A
Let us suppose that a traveller wants to go from city A to city B. Suppose, further, that the two cities are at a long distance from each other and also that there is no direct link between them. The
11. An absorbing state is one which once reached, does not allow transition to another state. Mark the statement as T (True) or F (False).
25. If a chain begins in a given transient state, t;, the probability that it shall eventually be absorbed in absorbing state a1 would be given by the ijth element of the "fundamental matrix" of the
1. What do you understand by Markov processes? In what areas of management can they be applied successfully?
2. What do you understand by transition probabilities? Is the assumption of stationary transition probabilities realistic, in your opinion? Why or why not?
3. Distinguish between a recurrent and an absorbing state. How can you tell in a transition matrix as to which states are recurrent and which are not?
4. Discuss the following assumptions in relation to the Markov chains:(i) Finite states(ii) First-order process(iii) Stationarity of transition probabilities(iv) Uniform time periods
5. How are steady state probabilities calculated? Do you agree that they are independent of the initial condition? Explain.
6. Explain how the probability tree helps to understand the problem of Markov processes.
8. Saddle point is the point of equilibrium. Mark the statement as T (True) or F (False).
7. Explain the method of calculation of ending up in each absorbing state when a chain begins in a particular transient state.
8. What is fundamental matrix of Markov chains? What does it calculate?
23. It is true to say that in equilibrium, the state probabilities in periodk, [Q(k)], are the same as the state probabilities in period k- 1, [Q (k- 1)]. Mark the statement as T (True) or F (False).
22. For a Markov process with two states, 1 and 2, transition probabilities as Pu, p 12 , p21 and p 22, the equilibrium probabilities q I and q2 can be obtained by solving the following pair of
12. Two states i andj are not communicative ifj is an absorbing state. Mark the statement as T (True) or F (False).
13. In a system, recurrent states are those which are not transient. Mark the statement as T (True) or F (False).
14. In a transition probability matrix, the sum of probabilities for each row and column is equal to 1. Mark the statement as T (True) or F (False).
15. A transition probability equal to 1 in a transition probability matrix indicates an absorbing state. Mark the statement as T (True) or F (False).
16. A market where only three brands of soft drinks are sold and the choice of a particular brand of soft drinks is assumed to depend on the choice in the immediately preceding time period, can be
17. The inputs required for Markovian analysis include the transition probabilities and the initial condition in which the given system is. Mark the statement as T (True) or F (False).
18. In a market with four brands of bread, the initial condition described by the vector[0.25 0.25 0.50 0] implies that, currently, the first two brands enjoy an equal share of the market, the third
19. The probability distributionofa system being indifferent states 1, 2, ... ,n, at any given time kgives the steady state probabilities, and is expressed as Q(k) = [qi(k) qi(k) ... qnCk)]. Mark the
20. Steady state probabilities are independent of time. Mark the statement as T (True) or F (False).
21. In a Markov chain with three states, 1, 2 and 3, with given transition probability matrix, P, the probability that the system, presently in state 3, shall be in the state 1, three periods from
9. "The Markov analysis may be understood as the way of analysing the past and present movement of some variable in an effort to forecast the future movement of that variable." Explain this statement
10. How can Markov analysis be used by a company to(i) predict its manpower needs;(ii) allocate service department overhead to production departments; and(iii) analyse its accounts receivables.
11. "The Markov chain method analyses the current behaviour of a process and relates the existing characters to the future." Elucidate this statement by taking examples from functional areas of
12. There are three firms ABC, PQR and XYZ sharing a market as 40%, 40% and 20% respectively on January 1, 2009. Over a Year, the following developments take place:ABC retains 80 per cent of its
13. A company is using Markov theory to analyse brand switching between three different brands of DVDs.Data has been obtained and used to estimate the following transition matrix for the probability
14. ABC Co. had 45% of the local market for its cosmetics, while the two other manufacturers XYZ Co.and PQR Co. have 30% and 25% shares, respectively, in the local market, as on 1st January of this
15. A transport company with a large fleet of buses periodically inspects the bearings on its buses and categorises them in one of the four states: (1) Good Bearings, (2) Lightly-worn Bearings, (3)
16. Formulate alternative Markov chain models for two policies for repairing a piece of equipment that must be finely adjusted. The equipment can be in any of three conditions: running ( or just
17. A manufacturing company has a certain piece of equipment that is inspected at the end of each day and classified as just overhauled, good, fair or inoperative. If the piece is inoperative, it is
19. A company has two production departments, P1 and P2 and three service departments, S1, S2 and S3•The direct cost allocated to each of the departments and percentage of total cost of each
18. ABC company has three service departments, S1, S2 and S3, and two production departments P1 and P2• Overhead is allocated to the production departments for inclusion in the stock valuation. The
20. A holding company Hhas two subsidiaries S1 and S2• The subsidiaries also own a portion of the share capital of H. The percentage ownership of the group is as given below:If the separately
21. A credit card company is attempting to determine a more effective set of credit control policies. It has traditionally classified all its accounts receivables into one of the five categories
11. On January 1 (this year), Bakery A had 30% of its local market share while the other two bakeries B and Chad 40% and 30%, respectively, of the market share. Based upon a study by a marketing
10. Three business magazines, Business Today, Business Line and Business Life, compete for advertising shares in a city. At the end of last year, Business Today had 40 per cent of the market while
24. The analysis of Markov chains with n states, out of which mare transient, requires decomposing the transition probability matrix into four sub-matrices: Q ( of the order n - m by n - m) matrix of
1. A person plays a game in which he gains Rs 20 with a probability of0.4 or loses Rs 10 with a probability of 0.6. He has an amount of Rs 20 with him and plays the game repeatedly until he loses all
35. The matrix below shows the paY-off in a 3 x 3 game between two players X and Y. Xis maximising player and Ythe minimising player.(a) Formulate a suitable Linear Programme model of the game with
2. A small city with 1,700 customers has three shoe stores S1, S2 and S3• Suppose that due to its location, there are no new customers added and the old ones also do not leave.A survey of the
A researcher is analysing switching between two competing products. The shares for the two products are found to be as given here:The researcher believes that an accurate representation of the market
4. The arrival behaviour of a bank employee reveals that ifhe is late on a day, he is 90 per cent sure to be in-time the next day. Similarly, ifhe is on time on a day, there is a 30 per cent chance
5. (a) The purchase patterns of two brands of toothpaste can be expressed as a Markov process with the following probabilities:(i) Which brand appears to have most loyal customers? Explain.(ii) What
Consider the following transition probability matrix:Without making calculations, can you say what would the market share of each of the firms, A, B and C be in equilibrium? Now, verify it by
7. In acitY, only two brands ofcola are sold:AA and BB. If a buyer bought cola AA lasttime, there is 0.75 chance that he would buy the same cola in the next purchase. Similarly, it is known that if a
9. A salesman makes all sales in three cities X, Y and Z only. It is known that he visits each city on a weekly basis and never visits the same city in successive weeks. Ifhe visits city X in a given
8. A researcher is analysing brand switching between different airlines, operating on the Delhi-Mumbai route by frequent fliers. On the basis of the data collected by her, the researcher has
1. What is game theory? State the assumptions underlying it. Discuss its importance to business decisions.
2. Given the following pay-off matrix of a zero-sum game, determine the optimal strategies for the players and the value of the game: A's strategy B's strategy b b b3 b4 a a2 569 2 50 8 -5 7 12 8 7
3. Is the following game strictly determinable? Is it fair? b b b3 b4 bs b6 a 18 8 18 8 18 8 15 6 15 6 15 6 az 18 8 18 8 18 8 -15 -6 -15 -6 -15 -6
4. You are given the paY-offmatrix in respect ofa two-person, zero-sum game, as follows:(a) Write the maximin and minimax strategies.(b) Is it a strictly determinable game?(c) What is the value of
5. For the following 'two-person, zero-sum' game, find the optimal strategies for the two players and value of the game:If the saddle point exists, determine it using the principle of dominance.
6. The two major scooter companies oflndia, ABC andXYZ, are competing for a fixed market. Ifboth the manufacturers make major model changes in a year, then their shares of the market do not
7. The squadron of Sqdn. Leader Kumar is equipped with six Big-27 fighters. The enemy is using X-16 fighters. In combat the two types of planes are matching and they fight to draw if they are in
8. M/S Godrej & Boyce and Hindustan Lever Ltd. have been selling competing products Cinthol and Liril respectively. The brand manager ofCinthol raised the following question:What should be the firm's
9. A partnership firm with two partners has a net worth of W. Each of the partners owns half of the business and, in addition, has a personal bank account of amount K. Of late, the partners are not
10. Two competing firms must open their next branch at one of the three cities: A, Band C, whose distance profile is given here. If both companies open their branches in the same city, they will
1. Find the saddle point, ifit exists, for each of the following games: (a) b 215 535 -5 b b3 8 2 6 1 3 943 b 552 @
11. How can a 'Two-Person, Zero-Sum Game' problem be converted into a linear programming problem?Illustrate with an example.
2. What do you understand by 'zero-sum' in the context of game theory? Can there be a non-zero-sum game also?
3. 'Game Theory provides a systematic quantitative approach for analysing competitive situations in which the competitors make use oflogical processes and techniques in order to determine an optimal
4. Explain the following:(a) saddle point (b) pure strategy (c) mixed strategy.Give the linear programming equivalent to a Game Theory problem.
5. What is a 'game' in game theory? What are the properties ofa game? Explain the "best strategy" on the basis of minimax criterion ofoptimalitY.
6. Describe the maximin and minimax principles of game theory.
7. Explain with examples the concept of dominance in games theory.
8. "The primary contribution of the game theory has been its concepts rather than its formal application to solving real problems." Explain.
9. "The two-person, zero-sum game is unrealistic." Elucidate the statement bringing out the limitations of game theory, if any.
10. What are the major limitations of game theory?
11. A and B play a game in which each has three coins: a 5 paise, 10 paise and 20 paise coin. Each player selects a coin without the knowledge of the other's choice. If the sum of the coins is an odd
12. Assume that two firms are competing for market share for a particular product. Each firm is considering what promotional strategy to employ for the coming period. Assume that the following
13. Two competitors are competing for the market share of the similar product. The paY-off matrix in terms of their advertising plan is as follows:Suggest the optimal strategies for the two
25. The effectivity of advertisement in different media by two competitive firms A and Bis given by the paY-offmatrix (in Rs '00) as follows:(i) Test whether there is a saddle point and a pure
26. There are two companies A and B in a certain city. Both companies have similar reputation and the total number of customers is equally divided between the two companies. Both the companies want
27. Solve the following zero-sum game where player B pays to player A: Player A Player B B B B3 BA B 23 -4 ++ 4 -4 64 -3 5 1 0 A -3
28. Solve graphically the following game: Player A B Player B B 3 4 A A2 -3 12 A3 6 -2 A4 -4 -9 A5 5 -3
29. Consider the following 'two-person, zero-sum' game:Suggest optimal strategies for the two players and the value of the game. Player A's strategies B Player B's strategies B B3 A 6 11 8 A 9 A3 7
30. Firm Xis fighting for its life against the determination of firm Yto drive it out of the industry. FirmX has the choice of increasing price, leaving it unchanged, or lowering it. Firm Y has the
31. Convert the following game problem into a linear programming problem. 5 Player A's Strategies 10 Player B's Strategies 7 4 6 2 260 9 0
32. Convert the following game problem, involving 'two-person, zero-sum game' into a linear programming problem:Don't solve. Player B -3 8 20 6 16 2289 Player A 0 4 12 21 -290
33. In respect ofa two-person, zero-sum game, the following paY-offmatrix is given:(a) Show that the above game has no saddle point.(b) Show that the game cannot be reduced by applying dominance
24. The following paY-off matrix describes increase in sales of Firm A from each of its strategies A 1, A2, A3, and A4 against each of the strategies B1, B2, B3 and B4 of the rival Firm B.Assuming a

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